If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4)

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Question has already given the value of f(4).  If  you clearly see, question has given the point (4, 3) it means the value of x = 4 and y = 3 so,

y = f(x)

3 = f(4)

And for f'(4):

Since, (4, 3) passes through the point (0, 2). We can find f'(4) by finding the slope so,

Slope of these point is given by

\(m = \frac{y2 – y1}{x2 – x1}\)

\(m = \frac{2 – 3}{0 – 4}\)

\(m = \frac{1}{4}\)

As we know, Slope is the derivative value of the equation

\(f'(4) = \frac{1}{4}\)

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