EunoR

2021-10-29

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

yagombyeR

Skilled2021-10-30Added 92 answers

The tangent to y=f(x) at (4,3)

This suggest that$(4,3)$ is a point on the graph of y=f(x)

Therefore,$f\left(4\right)=3$

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

$m=\frac{2-3}{0-4}=\frac{-1}{4}=0.25$

This is equal to f'(4)

Result: f(4)=3 and f'(4)=0.25

This suggest that

Therefore,

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

This is equal to f'(4)

Result: f(4)=3 and f'(4)=0.25

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