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Name: 1 Class: The graph of the derivative f of a function f is shown. (a) On what interval(s) is f increasing? (b) On what interval(s) is f decreasing? At what value(s) of x does f have a local maximum?
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How to fill out 1 derivative f
How to fill out 1 derivative f:
01
Begin by identifying the function, f, for which you want to find the derivative. For example, let's say f(x) = 2x^3 + 4x^2 - 6x + 1.
02
Use the power rule to find the derivative of each term in the function. For each term, multiply the coefficient by the exponent and decrease the exponent by 1. In our example, the derivative of 2x^3 is (3 * 2)x^(3-1) = 6x^2, the derivative of 4x^2 is (2 * 4)x^(2-1) = 8x, the derivative of -6x is (1 * -6)x^(1-1) = -6, and the derivative of 1 is 0 since it is a constant term.
03
Combine the derivatives obtained in the previous step. In our example, the derivative of f(x) = 2x^3 + 4x^2 - 6x + 1 is f'(x) = 6x^2 + 8x - 6.
04
You have now successfully filled out the derivative, f', of the given function, f.
Who needs 1 derivative f:
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