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Question

solve f'(x)=4x-3 when the curve passes (2,3)

Answer 1

f(x) = ∫f'(x)dx = ∫(4x - 3)dx = 2x² - 3x + C

 

Since the curve goes through the point (2, 3), f(2) = 3.

 

f(2) = 2(2)² - 3(2) + C = 3

 

So, 2 + C = 3

 

Therefore, C = 1

 

f(x) = 2x² - 3x + 1

Answer 2

You can determine the original function y=f(x) by taking the anti-derivative of f'(x), substituting x=2/y=3, and solving for C. 

 

However, if you just need to "solve for f'(x)", the slope of the f(x) function at any point x, then all you need to do is substitute 2 for x to get a slope value of 5 at the point (2,3).