Math CentralQuandaries & Queries


Question from Jasem:

Suppose that

(A) Find an equation for the tangent line to the graph of f(x) at x=2

(B) Find all values of xx where the tangent line is horizontal, and enter them as a comma-separated list (e.g., 2,-3,6). If there are none, enter none.

Values of x

Hi Jasem,

Use the power rule and the chain rule to differentiate

\[f(x) = (3x - 3)^{1/2}.\]

In the expression for $f^{\prime}(x)$ the term $(3x - 3)$ has a negative exponent. Write the expression for $f^{\prime}(x)$ as a fraction.

For (A) use the value of the derivative at $x = 2$ to write an equation for the tangent to $f(x)$ at the point $\left(2, f(2)\right).$

For (B) solve $f^{\prime}(x) = 0.$


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