ap-calculus-ab 1999 Q1

ap-calculus-ab · USA · free-response_formB Tangents, normals and gradients Chain Rule with Composition of Explicit Functions

Let $f$ be the real-valued function defined by $f ( x ) = \sqrt { 1 + 6 x }$. (a) Give the domain and range of $f$. (b) Determine the slope of the line tangent to the graph of $f$ at $x = 4$. (c) Determine the y -intercept of the line tangent to the graph of f at $\mathrm { x } = 4$. (d) Give the coordinates of the point on the graph of $f$ where the tangent line is parallel to $y = x + 12$.

answer and reason

Let $f$ be the real-valued function defined by $f ( x ) = \sqrt { 1 + 6 x }$.
(a) Give the domain and range of $f$.
(b) Determine the slope of the line tangent to the graph of $f$ at $x = 4$.
(c) Determine the y -intercept of the line tangent to the graph of f at $\mathrm { x } = 4$.
(d) Give the coordinates of the point on the graph of $f$ where the tangent line is parallel to $y = x + 12$.

Paper Questions

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