Home > Calculus > Slope of a Curve at a Point

How do you find the slope of the graph #f(x)=3x^3-6# at (2,18)?

Answer 1

Evelyn Agard

The value of the slope is #36#

The value of slope of a curve #f(x)# in #x_0# is #f'(x_0)#

Here we have:

#f'(x)=9x^2#

#f'(2)=9*2^2=9*4=36#

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Answer 2

Evelyn Agard

To find the slope of the graph of ( f(x) = 3x^3 - 6 ) at the point ( (2,18) ), you need to find the derivative of the function and then evaluate it at ( x = 2 ). The derivative of ( f(x) ) is ( f'(x) = 9x^2 ). When ( x = 2 ), ( f'(2) = 9(2)^2 = 36 ). So, the slope of the graph at ( (2,18) ) is ( 36 ).

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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.