Question

Consider the following curve. у 2x2 10x + 1 Find the slope m of the tangent line at the point (6, 13). m = Find an equation of the tangent line to the curve at the point (6, 13). y =

(a) Find the slope, m, of the tangent to the curve y = 8 + 5x2 – 2x3 at the point where x = a. m =
(b) Find equations of the tangent lines at the following points. (1, 11) y = (2, 12) y =

Answer 1

The slope (m) of the tangent line at the point (6, 13) for the curve y = 2x^2 - 10x + 1 is 14, and the equation of the tangent line is y = 14x - 71.

Step-by-step explanation:

The slope (m) of the tangent line to a curve at a given point can be found by taking the derivative of the function representing the curve and evaluating the derivative at that specific point.

For the specific curve y = 2x2 - 10x + 1, we will calculate its derivative and then plug in the x-value of the point (6, 13) to find the slope of the tangent line at that point.

Step 1: Differentiate the function with respect to x: y' = 4x - 10.

Step 2: Evaluate the derivative at x = 6: m = 4(6) - 10 = 14.

The slope m of the tangent line at the point (6, 13) is 14.

To find the equation of the tangent line, we use the point-slope form y - y1 = m(x - x1):

y - 13 = 14(x - 6).

Simplify to get the equation of the tangent line: y = 14x - 71.