Brief Calculus.

Question

The slope of the tangent line to the parabola y = 2x^2 - 5x + 7 at the point where x = 5 is: ............................

The equation of this tangent line can be written in the form y = mx + b where m is: ....................................

and where b is: .......................

Answer 1

y^' = 4x - 5 so y^'(5) = 20 - 5 = 15 is the slope of the tangent line to the parabola at x = 5.

The equation of the tangent line can be found, after calculating the y-coordinate on the parabola at x=5:

y(5) = 2·25 - 5·5 + 7 = 32 so the point on the parabola and tangent line is (5,32).

The tangent line's equation can be found in pt-slope form: y - 32 = 15·(x - 5) then converted to slope-int form:

y = 15x - 43 where m = 15 and b = - 43