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

EunoR 2021-10-29 Answered
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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## Expert Answer

yagombyeR
Answered 2021-10-30 Author has 23648 answers
The tangent to y=f(x) at (4,3)
This suggest that $$\displaystyle{\left({4},{3}\right)}$$ is a point on the graph of y=f(x)
Therefore, $$\displaystyle{f{{\left({4}\right)}}}={3}$$
Slope of the tangent at x=4 to y=f(x) is f'(4)
Since the tangent passes through (4,3) and (2,0), its slope is equal to
$$\displaystyle{m}={\frac{{{2}-{3}}}{{{0}-{4}}}}={\frac{{-{1}}}{{{4}}}}={0.25}$$
This is equal to f'(4)
Result: f(4)=3 and f'(4)=0.25

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