Find the function f given that the slope of the tangent line at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=5(2x − 1)^{4}, (1, 9)

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attend ance had been 27,000.When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?

Determine whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) ${\displaystyle f\left(x\right)=-3x^2+7}$

c) $f(x)=\frac{x+1}{x+2}$
${\displaystyle d)f\left(x\right)=x^5+1}$

Find the linear approximation of the function $f(x)=\sqrt{1-x}$ at $a=0$ and use it to approximate the numbers $\sqrt{0.9}$ and $\sqrt{0.99}$.

What is the minimum vertical distance between the parabolas ${\displaystyle y=x^2+1}$ and ${\displaystyle y=x-x^2}$

Find the Laplace transform of ${\displaystyle f\left(t\right)=\left(\sin t–\cos t\right)2}$

Find the values of b such that the function has the given maximum or minimum value.
${\displaystyle f\left(x\right)=-x^2+bx-75}$; Maximum value: 25

Plot the complex number and find its absolute value.
z=9i