# x^{4}(x^{2}-3)^{6}sin^{2}8x

Question
Functions
$$x^{4}(x^{2}-3)^{6}\sin^{2}8x$$

2021-01-24
If the question is to find the zeros of the function, then here is the answer.
We have $$x^{4}(x^{2}−3)^{6}\sin^{2}8x=0$$ only when
$$x^{4}=0, or, x^{2}-3)^{6}=0, or, sin^{2}8x=0$$
This is equivalent to
$$x=0, or, x^{2}-3 = 0, or, \sin8x=0$$
We know that sine function is zero for angles nπ,nπ, where nn is an integer. Therefore, we get
$$x=0, or, x=\pm\sqrt3, or, x = \frac{8}{n\pi}.$$
If you need more explanation, or wanted something else then feel free to leave a comment. I will update the answer accordingly. ​

### Relevant Questions

The graph of y = f(x) contains the point (0,2), $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}$$, and f(x) is greater than 0 for all x, then f(x)=
A) $$\displaystyle{3}+{e}^{{-{x}^{{2}}}}$$
B) $$\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}$$
C) $$\displaystyle{1}+{e}^{{-{x}}}$$
D) $$\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}$$
E) $$\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}$$
Find f'(a)
$$\displaystyle{f{{\left({t}\right)}}}={\frac{{{3}{t}+{3}}}{{{t}+{2}}}}$$
$$\displaystyle{x}^{{{4}}}{\left({x}^{{{2}}}-{3}\right)}^{{{6}}}{{\sin}^{{{2}}}{8}}{x}$$
Use the theorems on derivatives to find the derivatives of the following function:
$$\displaystyle{f{{\left({x}\right)}}}={\left({5}{x}^{{{3}}}+{8}{x}^{{{2}}}-{4}\right)}^{{{4}}}{\left({8}{x}^{{{4}}}-{2}{x}^{{{3}}}-{7}\right)}$$
Solve the given system of linear equations.
$$\displaystyle{\frac{{{1}}}{{{2}}}}{x}-{\frac{{{3}}}{{{4}}}}{y}={0}$$
8x-12y=0
(x,y)=

Polynomial equation with real coefficients that has the roots $$3, 1 -i\ \text{is}\ x^{3} - 5x^{2} + 8x - 6 = 0.$$

Find the equation of the tangent plane to the graph of $$\displaystyle{f{{\left({x},{y}\right)}}}={8}{x}^{{{2}}}-{2}{x}{y}^{{{2}}}$$ at the point (5,4).
A)z=23x-15y+42
B)z=48x-80y+120
C)0=48x-80y+120
D)0=23x-15y+42
Which relation does not represent a function?
$$A. (0,8), (3,8), (1,6)$$
$$B. (4,2), (6,1), (8,9)$$
$$C. (1,20), (2,23), (9,26)$$
$$D. (0,3), (2,3), (2,0)$$
$$\displaystyle{A}.{\left({0},{8}\right)},{\left({3},{8}\right)},{\left({1},{6}\right)}$$
$$\displaystyle{B}.{\left({4},{2}\right)},{\left({6},{1}\right)},{\left({8},{9}\right)}$$
$$\displaystyle{C}.{\left({1},{20}\right)},{\left({2},{23}\right)},{\left({9},{26}\right)}$$
$$\displaystyle{D}.{\left({0},{3}\right)},{\left({2},{3}\right)},{\left({2},{0}\right)}$$