How do you find the derivative of #y=2x^2-7#, where x=-2?

Answer 1

#-8#

differentiate using the #color(blue)"power rule"#

#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(ax^n)=nax^(n-1)" and " d/dx("constant")=0)color(white)(a/a)|)))#

#y=2x^(color(red)(2))-7rArrdy/dx=(color(red)(2)xx2)x^(color(red)(2)-1)+0=4x#

when x = -2: #dy/dx=4(-2)=-8#

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Answer 2

Christopher Agresta

To find the derivative of ( y = 2x^2 - 7 ) at ( x = -2 ), we first differentiate the function with respect to ( x ) using the power rule, then evaluate the derivative at ( x = -2 ).

The derivative of ( y = 2x^2 - 7 ) is ( \frac{dy}{dx} = 4x ).

Substituting ( x = -2 ) into the derivative expression, we get ( \frac{dy}{dx} = 4(-2) = -8 ). Therefore, the derivative of ( y = 2x^2 - 7 ) at ( x = -2 ) is ( -8 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.