Question

find the slope of the curve ( y = - 7 x ^ { 2 } ) at ( ( - 4, - 112 ) ).

the slope of the curve ( y = - 7 x ^ { 2 } ) at ( ( - 4, - 112 ) ) is ( square ). (simplify your answer.)

Explanation:

Step1: Differentiate the function

Use the power rule \(\frac{d}{dx}(x^n)=nx^{n - 1}\). For \(y=-7x^{2}\), \(y^\prime=\frac{d}{dx}(-7x^{2})=-7\times2x=-14x\).

Step2: Substitute \(x = - 4\) into the derivative

Substitute \(x=-4\) into \(y^\prime=-14x\). Then \(y^\prime|_{x = - 4}=-14\times(-4)\).

Answer:

\(56\)