A "zoom" on the graph of y = f(x) near (xo, Yo) (with yo = f(xo)) with magnification factor M (the same in both r and y directions) is the graph of the function defined by f(ro + x/M) = yo + y/M. Prove that if f is differentiable at x0, then the zoom converges to the straight line through the origin with slope f'(xo), as M → o. What happens to the zoom of Jx| near the origin?

Q: f (x) = a?2 + bx + c  mtan =f’= 2ax + b   At what value(s) of x is the line tangent to the graph of…

A:

Q: Find the slope of the tangent line to the curve y=1+1x at x =2. Do not use the derivative but rather…

A: Please see the below picture for detailed solution.

Q: find the tangent line of f(x)= 3x-4/x+1 at x=0

A:

Q: The slope 'mi of the tangent to the curvez= 3(5t+1)*andy=10+2 at t=2is,

A:

Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

A:

Q: Let f (æ) = (In(z³ + 1))". Find the slope of the tangent line at x = 1. (Give your final answer as a…

A: The slope of tangent to a curve y=f(x) at a point x=a is given by f'(a)

Q: In each part, list the points (A–F) on the graph of f whose x-coordinates satisfy the given…

A: Given data: The given graph is shown. Point A on the graph has zero slope and maximum value of the…

Q: The tangent line at x = 4 on the graph of f(x) is given as y = 2x - 7.

A:

Q: 3. If f is the function given by f(x) = -x³ + x² + 3x-2, name the open interval where the graph of f…

A:

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

A:

Q: Suppose the slope of the curve y = f¯¹ (x) at the point (4,7) is . Find ƒ'(7). [B] 4 [A] 1 [C] 5 [D]…

A:

Q: Find the slope of the tangent line of f (x) = 2x² - 3x + 2 at x = 2 %3D

A:

Q: Let f(x) = /25 - æ The slope of the tangent line to the graph of f(x) at the point (9, 4) is

A:

Q: Find the concave up and down intervals of the function f''(x)= 6/(x-1)3. Then identify any points of…

A:

Q: Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope 4/x

A: