Compute the right-hand derivative D-f(0)= lim f(h) - f(0) h→0t h 4x + 7 if x<0 {f(x) = 7x +8 if x ≥0 The right-hand derivative is =

Q: Find the difference quotient en-7 for each of the given functions. B. f(x) = 3x + 2 Find the slope…

A: Solution

Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: xy2+5x2-3y2+45=0  (1,5)   Evaluate the derivative at the given function point.

A: We have to find derivative

Q: Graph y = - x“ + 2x² – 10 function using x- and y-intercepts, critical points, points of inflection,…

A: Plot the graph for f(x).

Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

A:

Q: Calculate derivative F(x) = (7-10x) (7+10x) by expanding or simplifying the function df/dx

A:

Q: Give two applications of the derivative f(x + h) - f(x) f'(x) = lim h

A: The given function f'x=limh→0f(x+h)-f(x)h is the derivative by first principle.

Q: Find the derivative f(x) = √(7 + 4x2) - (1)/(5x2 + 9).

A: Consider the provided function, fx=7+4x2-15x2+9 Find the derivative of the function.…

Q: Use the chain rule to find the derivative of f(x)=10√10x^10+2x^9

A: Consider the given function: fx=1010x10+2x9 Chain rule says that: ddxfgx=ddgxfgx+dgxdx We have,…