Problem

Find f such that f′(x)=10x−7,f(9)=0

Answer

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Answer

f(x)=5x2−7x−342 is the final answer.

Steps

Step 1 ：Given the derivative of the function f′(x)=10x−7 and a point on the function (9,0).

Step 2 ：Integrate the derivative to find the function f(x). The integral of 10x−7 is 5x2−7x+C, where C is the constant of integration.

Step 3 ：Substitute the point (9,0) into the function to solve for C. So, 0=5∗92−7∗9+C. Solving this equation gives C=−342.

Step 4 ：Substitute C=−342 back into the function to get the final function f(x)=5x2−7x−342.

Step 5 ：f(x)=5x2−7x−342 is the final answer.

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