Find the function whose tangent has slope 𝑥 3 − 2 𝑥 2 + 16 for each of x and whose graph passes through the point (2,5).

Question

Find the function whose tangent has slope 𝑥 3 − 2 𝑥 2 + 16 for each of x and whose graph passes through the point (2,5).
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Solution 1

The function whose tangent has a given slope is the integral of that slope. The slope given is x^3 - 2x^2 + 16.

Step 1: Integrate the slope function to find the original function.

∫(x^3 - 2x^2 + 16) dx = (1/4)x^4 - (2/3)x^3 + 16x + C

This is the general form of the function. The constant C can Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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