Question

the polynomial function ( f(x)=2 x^{2}+8 x - 7 ) has a critical point at which of the following ( x )-values?

a. ( x = 0 )
b. ( x=-2 )
c. ( x=-7 )
d. ( x = 2 )

Explanation:

Step1: Find the derivative of the function

The derivative of \(F(x)=2x^{2}+8x - 7\) using the power rule \((x^{n})^\prime=nx^{n - 1}\) is \(F^\prime(x)=\frac{d}{dx}(2x^{2})+\frac{d}{dx}(8x)-\frac{d}{dx}(7)\).

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Step2: Set the derivative equal to zero and solve for \(x\)

Set \(F^\prime(x)=0\), so \(4x+8 = 0\).
Subtract \(8\) from both sides: \(4x=-8\).
Divide both sides by \(4\): \(x=\frac{-8}{4}=-2\)

Answer:

B. \(x = - 2\)