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

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