Homework SourseFor the given function find a the equation of the secant lin
For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y=f(x)=x^2+x; x=-1, x=2 (a) The equation of the secant line is y=______ (b) The equation of the tangent line is y=_____ type your answer in slope intercept form
Solution
(a) y=f(x)=x^2+x; x=-1, x=2 f(-1) = (-1)^2+(-1) = 0 f(2) = (2)^2 + 2 = 6 Now we have two points on the line (-1,0) and (2,6). Using these points, we can calculate the slope: (6-0)/(2-(-1)) = 2 Now we build the equation using point-slope form (y-6) = 2(x-2) And then solve for y. y=2x+2 (b) To calculate the slope at x=-1, we take the derivative of f(x) f\'(x) = 2x+1 and plug in -1 f\'(-1) = 2(-1) + 1 = -1 And again use point-slope form: (y-0) = -1(x-(-1)) y = -x - 1
