# Recent questions in Analyzing functions

Analyzing functions

### Let $$g(x) = \int_0^x f(t) dt$$ where f is the function whose graph is shown in the figure. (a) Estimate g(0), g(2), g(4), g(6), and g(8). (b) Find the largest open interval on which g is increasing. Find the largest open interval on which g is decreasing. (c) Identify any extrema of g. (d) Sketch a rough graph of g.

Analyzing functions

### At what point does the curve have maximum curvature? What happens to the curvature as x tends to infinity $$y=\ln x$$

Analyzing functions

### For which nonnegative integers n is $$n^2\leq n!?$$

Analyzing functions

### Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. $$f(x,y)=x^3-6xy+8y^3$$

Analyzing functions

### Polynomial function's f(x) coefficients are real numbers. Find the remaining zeros of f. Degree 6, zeros: i, 3 - 2i, -2 + i

Analyzing functions

### Find an nth-degree polynomial function with real coefficients satisfying the given conditions. Verify the real zeros and the given function value. n = 3, 2 and 2 - 3i are zeros, f(1) = -10

Analyzing functions

### Evaluate the indicated expressions and simplify. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{1},{f{{\left({x}+{2}\right)}}},{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}.$$

Analyzing functions

### Find the $$\displaystyle{\left({f}+{g}\right)}{\left({x}\right)}{\quad\text{and}\quad}{\left({f}–{g}\right)}{\left({x}\right)}$$, if $$\displaystyle{f{{\left({x}\right)}}}={10}{x}–{8}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={5}{x}+{7}$$

Analyzing functions

### Find all values $$x = a$$ where the function is discontinuous. $$\displaystyle{f{{\left({x}\right)}}}={8}{x}^{{2}}+{8}{x}+{4}.$$

Analyzing functions

### Find the region enclosed by the curves $$\displaystyle{x}={3}{y}^{{2}}{\quad\text{and}\quad}{x}={y}^{{2}}+{7}$$ List the points of intersection of these curves from bottom to top in the form (x, y).

Analyzing functions

### Find the difference quotient of f, that is, find $$\displaystyle\frac{{{f{{\left({x}+{h}\right)}}}−{f{{\left({x}\right)}}}}}{{h}},{h}≠{0}$$, for each function. Be sure to simplify. $$\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{{x}+{3}}}$$

Analyzing functions

### Find the derivative of the function $$\displaystyle{f{{\left({x}\right)}}}={\ln{{\left({e}^{{x}}+{12}\right)}}}$$

Analyzing functions

### The function f(x) is linear. Write a formula for f(x) that satisfies the conditions: slope $$\displaystyle=-\frac{{3}}{{4}}$$, y-intercept $$\displaystyle=\frac{{1}}{{3}}$$

Analyzing functions

### What period do the sine, cosine, cosecant, and secant functions have? What period do the tangent and cotangent functions have?

Analyzing functions

### Is the statement true or false? "The domain and the range of the reciprocal function are the set of all real numbers."

Analyzing functions

### Find the vertex, focus, and directrix for the parabolas: a) $$\displaystyle{\left({y}–{9}\right)}^{{2}}={8}{\left({x}-{2}\right)}$$ b) $$\displaystyle{y}^{{2}}–{4}{y}={4}{x}–{2}^{{2}}$$ c) $$\displaystyle{\left({x}–{6}\right)}^{{2}}={4}{\left({y}–{2}\right)}$$

Analyzing functions

### Sketch the graph of the function $$\displaystyle{f{{\left({x}\right)}}}=-{x}^{{3}}+{3}{x}^{{2}}–{7}$$. List the coordinated of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down.

Analyzing functions

### Which one of the following function has an inverse? $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}},{g{{\left({x}\right)}}}={x}^{{3}}$$

Analyzing functions