Consider a function $f$. The line $L_{1}$ with equation $y=3 x+1$ is a tangent to the graph of $f$ when $x=2$.
(a) (i) Write down $f^{\prime}(2)$.
(ii) Find $f(2)$.

Answer

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Answer

$\boxed{f(2) = 7}$

Steps

Step 1 ：Find the slope of the tangent line $L_1$ at $x=2$ from its equation: $y=3x+1$. The slope is the coefficient of $x$, so $f'(2) = 3$

Step 2 ：Find the value of $y$ on the tangent line $L_1$ at $x=2$: $y = 3(2) + 1 = 7$. Since the tangent line touches the graph of $f$ at $x=2$, we have $f(2) = 7$

Step 3 ：$\boxed{f'(2) = 3}$

Step 4 ：$\boxed{f(2) = 7}$

Consider a function $f$. The line $L_{1}$ with equation $y=3 x+1$ is a tangent to the graph of $f$ when $x=2$.(a) (i) Write down $f^{\prime}(2)$.(ii) Find $f(2)$.

Answer

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Consider a function $f$. The line $L_{1}$ with equation $y=3 x+1$ is a tangent to the graph of $f$ when $x=2$.
(a) (i) Write down $f^{\prime}(2)$.
(ii) Find $f(2)$.