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Solve the following.
The function f is defined for all x ∈ mathbbR. The line with equation y = 6x - 1 is the tangent to…
The function $f$ is defined for all $x \in \mathbb{R}$. The line with equation $y = 6x - 1$ is the tangent to the graph of $f$ at $x = 4$.
(i)[1]
Write down the value of $f'(4)$.
(ii)[1]
Find $f(4)$.
Answer
Answer (i)
The slope of the tangent at $x = 4$ is $f'(4)$, and the tangent $y = 6x - 1$ has slope $6$.
Final answer: 6
Answer (ii)
The tangent touches the graph at $x = 4$, so $f(4) = 6(4) - 1 = 23$.
Final answer: 23