find the equation of the function that has 𝑓′(𝑥)=6𝑥3+𝑥+7𝑓′(𝑥)=6𝑥3+𝑥+7 and passes through the point (0,4)
Question
Solution 1
The given derivative function is f'(x) = 6x^3 + x + 7.
To find the original function f(x), we need to integrate the derivative function.
∫f'(x) dx = ∫(6x^3 + x + 7) dx = (6/4)x^4 + (1/2)x^2 + 7x + C.
So, f(x) = (3/2)x^4 + (1/2)x^2 + 7x + C.
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