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Use the definition of the derivative to find the slope of the tangent line to the graph of the given function at any point. Show your work by completing the four-step process. (Simplify your answers completely for each step.) f(x) = 4x² + 7x Step 1: Step 2: Step 3: Step 4: f'(x) = lim h→0 f(x + h) = 4(x + h)² +7(x+h) f(x + h)-f(x) = h(4(2x+h)+7) f(x + h) − f(x) = h f(x+h)-f(x) h 4(2x+h) +7 8x + 7 X X (Expand your answer completely.) (Factor your answer completely.)
Let f(x) = x² + 5x. (a) Find the derivative f' off by using the definition of the derivative. Show your work by completing the four-step process. (Simplify your answers completely for each step.) f(x + h) = (x + h) +5(x+h) (b) Step 1: Step 2: Step 3: Step 4: f'(x) = _lim_ h→0 f(x +h)-f(x) = f(x+h)-f(x) h f(x +h)-f(x) h (Expand your answer completely.) X (Factor your answer completely.) Find an equation of the tangent line to the graph of f at the point (1,4). Give your answer in the slope-intercept form.