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. So, we first need to find the integral of the given function, x^3 - 2x^2 + 16.

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

Now, we know that the graph of the function passes through the point (2,5). We can use th 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.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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