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- Graph the function Y2=nDeriv (“originalfunction”,X,X). By doing this, you’re having the calculator evaluate the derivative numerically at each point and graph the results. For each function: f(x)=x2+2x-1 g(x)= -500/x, x ≠0 k(x)= |x-2|arrow_forwardThe graph of f(x) passes through the point (4,0). The slope of the line tangent to the graph at the point (4, 0) is −2x (x-4)² x→4 f(x) 3. Evaluate limarrow_forwardIf we need to calculate the derivative of a function at a point, there are two ways we can think about doing this. For example suppose f() = x – x, and we need to determine the value of f(4). One option is to just calculate the derivative at that point by plugging the point into the limit definition, like this: f(4 + h) – f(4) ( (4 + h)² – (4 + h)) - (4² – 4) f'(4) = lim (16 + 8h + h2 -4 – h) - (16 - 4) lim 7h + h2 = lim h(7+ h) lim h = lim h→0 h lim 7+h = 7. || h h h Another option is to calculate f'(x) in terms of x, and then plug in a value for x at the end, like this: f(x + h) – f(x) (2+ h) – (x + h)) - (2² – a) (22 + 2xh + h² – z – h) – (22 – 2) lim f'(x) = lim = lim 2xh + h2 - h h(2x + h - 1) = lim h 0 h h = lim = lim h h h that is to say, f'(x) = 2x – 1, and therefore f'(4) = 2(4) – 1 = 7. Notice that we get the answer f'(4) = 7 both ways. The second approach might look somewhat more complicated at first, but it turns out to be much more efficient if we ever need to know the…arrow_forward
- Prob. 6 (a) (10 point) Let f(x) = 2x² – 3. Find ƒ'(−2) using only the limit definition of derivatives. (b) (10 p.) If ƒ(x) = √√x + 6, find the derivative f'(c) at an arbitrary point c using only the limit definition of derivatives.arrow_forwardFor the function f(x) = 8x² + 10x + 24, find f' (x) using the f(x + h) – f(x) definition lim h→0 h 20x + 24 16x + 10 8x 16x 8х + 10arrow_forwardf(x)=x2+2x-1 g(x)= -500/x, x ≠0 k(x)= |x-2| For each function, do the following: Graph the derivative, f ′(x), on your calculator by assigning it to the function Y1. Draw the graphs that you create on your calculator. Make sure to label and submit them along with the rest of the assignment.arrow_forward
- For the function f(x) = 4x + 19x + 28, find f'(x) using the f(x +h)- f(x) definition lim O 4r 8x O 8r O 38x +28 O 8&r + 19 O 4c + 19arrow_forwardSuppose that f(x) and g(x) are two functions and we know that: f(-3) = 2 g(-3) = 5 f'(-3) g'(-3) Find the following: (ƒ − g)'(−3) = (g - f)'(-3) = -1 -2 == (fg)'(-3) = (4) - '(-3) = f(x) x² If k(x) = = = then k'(-3)arrow_forward