Find the tangent line to the graph y=20+5x^2-17x at the point (3,14).?

Question

Find the tangent line to the graph y=20+5x^2-17x at the point (3,14). The equation y=____x+ ____ is the desired tangent line

Answer 1

y' = 10x - 17 = 30-17 = 13 at (3, 14)
y = 13(x-3) + 14 = 13x - 25

Answer 2

take the 1st by-product and set it equivalent to 0, then sparkling up this for x, which provides an x fee on the tangent line; plug this fee decrease back into the unique equation to acquire a corresponding y fee. Now you have this element and additionally the element (3, 14), and using those 2 factors, you may confirm a numerical fee for the slope. after that, use element-slope variety with the element (3,14) to confirm the equation by way of that element.

Answer 3

f `(x) = 10x - 17
f `(3) = 30 - 17
f `(3) = 13
m = 13
y - 14 = 13(x - 3)
y = 13x - 39 + 14
y = 13x - 25