16. [-/0.33 Points] DETAILS SCALCET8 2.7.AE.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Video Example () EXAMPLE 1 Find an equation of the tangent line to the parabola y = 5x2 at the point P(4, 80) using this definition. SOLUTION Here we have a = 4, and f(x) = 5x2, so the slope is m = lim f ( x) - f( 4 ) X - 4 x - 4 = lim X - 4 X - 4 = lim 5(x - 4) X - 4 X - 4 = lim 5 X - 4 + 20 = Using the point slope form of the equation of a line, we find an equation of the tangent line at (4, 80) is y - [ =Q( -)) or y =x-[17. [-/0.33 Points] DETAILS SCALCET8 2.7.AE.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Video Example () EXAMPLE 4 Find the derivative of the function f(x) = x2 - 7x + 5 at the number a. SOLUTION From the definition we have f'(a) = lim f(a + h) - f(a) h - 0 h = lim - 7 (a + h) + 5 - [a2 - 7a + 5] h - 0 h + - 7a - 7h + 5 - a2 + 7a - 5 = lim h - 0 h = lim h - 0 h = lim h - 0