`f'(x) = 4, (0,1)` Find a function `f` that has the derivative `f'(x)` and whose graph passes through the given point. Explain your reasoning.

Textbook Question

Chapter 3, 3.2 - Problem 70 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to notice that if the derivative is a constant function, then the primitive is a linear function, such that:

`f(x) = ax + b`

Differentiating f(x) yields:

`f'(x) = a`

You need to set equal 4 and a such that:

`a = 4`

You should notice that b is not determined, yet. You may find out b using the information that the function passes through the point (0,1), such that:

`f(0) = 1 => f(0) = a*0 + b`

`b = 1`

Hence, evaluating the function under the given conditions, yields `f(x) = 4x + 1`

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