A) find the slope of the tangent line to the graph of f(x) = -3x^2 +7 at the point x = -2. you must use limits to do this. b) write the equation of the tangent line at x = -2. c) graph f(x) and the tangent line. does it seem reasonable?

Refresh if you see errors in the explanation.======(a)the slope of the tangent line to the graph of  at the point  is given by the following difference quotient:     let us calculate  and  separately,with  , we have    and we also have    bringing these together into the limit:     so the slope of the tangent line is 12======(b)to write the equation of the tangent line at x = -2, we need the y-coordinate on the graph. we only have the x-coordinate, -2, and the slope, 12.to find the corresponding y-coord, plug x=-2 into the function. we already did this before but    so the point on the graph in question is (-2,-5). using point-slope form of a line:     they do not ask for slope-intercept form, so we can leave it. you might want to change it if you need to graph it though.======(c)use a graphing calculator. i use desmos, but if you want to use a handheld graphing calculator like texas instruments, you may want to move the tangent line equation into    to graph it.it looks reasonable.