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

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

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

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)