Additional+Example

Find the equation of a tangent line to the function f(x) = 4x 2 + 7x +5 at x = 3

First we need to find the general slope of the tangent line. We do this by deriving the original function. We identify the rule(s) needed to derive the function and then derive. The derivation of f(x) is **8x + 7**.
 * Step 1: Derive**

At x = 3, the slope of the tangent line is 8(3) + 7 = **31**. This is our slope at x = 3.
 * Step 2: Find Slope at Given Point**

Point-Slope form is (y - y 1 ) = m(x - x 1 ) where m is the slope. Substitute the coordinates and slope, and solve the equation for y.
 * Step 3: Find Equation using Point-Slope form.**

(y - 62) = 31(x - 3) y - 62 = 31x - 93 This is the equation of the tangent line.
 * y = 31x - 31**

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