${f}^{\prime}(0)\text{for}f(x)={x}^{\frac{5}{3}}sgn\text{}x$

Trystan Castaneda
2022-08-16
Answered

Find the following. Explain your answer

${f}^{\prime}(0)\text{for}f(x)={x}^{\frac{5}{3}}sgn\text{}x$

${f}^{\prime}(0)\text{for}f(x)={x}^{\frac{5}{3}}sgn\text{}x$

You can still ask an expert for help

Kelton Glover

Answered 2022-08-17
Author has **17** answers

Solution: $f(x)={x}^{\frac{5}{3}}sgn\text{}x$

$\{\begin{array}{ll}-1& x<0\\ 0& x=0\\ 1& x>0\end{array}$

$\frac{d}{dx}({x}^{n})=n{x}^{n-1}$

Now, ${f}^{\prime}(x)=sgn\text{}x\frac{d}{dx}({x}^{\frac{5}{3}})+{x}^{\frac{5}{3}}\frac{d}{dx}(sgn\text{}x)\phantom{\rule{0ex}{0ex}}=sgn\text{}x\frac{5}{3}\times \frac{1}{3}+{x}^{\frac{5}{3}}\times 0\phantom{\rule{0ex}{0ex}}{f}^{\prime}(0)=0+0=0$

$\{\begin{array}{ll}-1& x<0\\ 0& x=0\\ 1& x>0\end{array}$

$\frac{d}{dx}({x}^{n})=n{x}^{n-1}$

Now, ${f}^{\prime}(x)=sgn\text{}x\frac{d}{dx}({x}^{\frac{5}{3}})+{x}^{\frac{5}{3}}\frac{d}{dx}(sgn\text{}x)\phantom{\rule{0ex}{0ex}}=sgn\text{}x\frac{5}{3}\times \frac{1}{3}+{x}^{\frac{5}{3}}\times 0\phantom{\rule{0ex}{0ex}}{f}^{\prime}(0)=0+0=0$

asked 2021-09-07

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

a)

b)

c)

asked 2021-06-11

Find the linear approximation of the function

asked 2021-09-10

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?

asked 2021-05-14

Find the absolute value.

|8i|

|8i|

asked 2021-06-03

Given $h\left(x\right)=2x\xb2-4x+5$ , find h(-4).

asked 2022-08-05

If 4 is a zero of $f(x)=3{x}^{3}+kx-2$ find the value of k

asked 2022-01-19

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. 2i, 1-i