get f′(−8) = = . This simplifies to f′(−8) = = 4.
If you noticed that the function is simply the equation of a line, then you would have seen that
the derivative is simply the slope of the line, which is 4 everywhere.- −10
We find the derivative of a function, f(x), using the definition of the derivative, which is: f′(x) =. Here f(x) = 5x^2 and x = −1. This means that f(−1) = 5(−1)^2 = 5 and f
(−1+ h) = 5(−1+ h)^2 = 5(1 − 2h + h^2 ) = 5 − 10h + 5h^2 . If we now plug these into the definitionof the derivative, we get f′(−1) = = . Thissimplifies to f′(−1) = . Now we can factor out the h from the numerator andcancel it with the h in the denominator: f′(−1) = (−10 + 5h). Now wetake the limit to get f′(−1) = (−10 + 5h) = −10.- 16 x
We find the derivative of a function, f(x), using the definition of the derivative, which is: f′(x) =. Here f(x) = 8x^2 and f (x + h) = 8(x + h)^2 = 8(x^2 + 2xh + h^2 ) = 8x^2 +16xh
+ 8h^2 . If we now plug these into the definition of the derivative, we get f′(x) = = . This simplifies to f′(x) = . Now we can factor out the h from the numerator and cancel it with the h in the
denominator: f′(x) = (16x + 8h). Now we take the limit to get f′(x) = (16x + 8h) = 16x.- −20x
We find the derivative of a function, f(x), using the definition of the derivative, which is f′(x) =