Question

let $h(x)=3x^{4}-5x^{3}+2x^{2}$. find $h(-1)$. choose 1 answer: a -9 b -10 c -31 d 9

Explanation:

Step1: Differentiate $h(x)$

Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, if $h(x)=3x^{4}-5x^{3}+2x^{2}$, then $h'(x)=3\times4x^{3}-5\times3x^{2}+2\times2x = 12x^{3}-15x^{2}+4x$.

Step2: Substitute $x = - 1$ into $h'(x)$

$h'(-1)=12(-1)^{3}-15(-1)^{2}+4(-1)$.

Step3: Calculate the result

$h'(-1)=12\times(-1)-15\times1 + 4\times(-1)=-12 - 15-4=-31$.

Answer:

C. - 31