Home > Calculus > Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

Is #f(x)=(2x+4)^2-6x-7 # increasing or decreasing at #x=-2 #?

Answer 1

decreasing

f '(x)= 2(2x+4) *2 -6. First, find f '(x). If f '(-2) is positive, then f(x) is increasing; if it is negative, then f(x) is decreasing.

Since f '(-2) = -6, f(x) is decreasing.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Adam Adkins

To determine if the function ( f(x) = (2x + 4)^2 - 6x - 7 ) is increasing or decreasing at ( x = -2 ), we need to evaluate the sign of the derivative of the function at that point.

First, find the derivative of ( f(x) ) with respect to ( x ):

[ f'(x) = 2(2x + 4)(2) - 6 ]

[ = 8x + 16 - 6 ]

[ = 8x + 10 ]

Now, evaluate ( f'(-2) ):

[ f'(-2) = 8(-2) + 10 ]

[ = -16 + 10 ]

[ = -6 ]

Since the derivative ( f'(-2) ) is negative, the function ( f(x) ) is decreasing at ( x = -2 ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.