2. The graph of the derivative function f'(x) of a function f(x) a) Determine: the intervals where f(x) is increasing; the intervals where f(x) is decreasing; the x -coordinate for all local extrema of f(x);

Q: If f(x)=4/x, find the derivative of f(x) at x=2 using the limit definition of the derivative at a…

A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

Q: g(x) = In tanh-1 x

A:

Q: Using the limit definitoin of the derivative, comput the derivative of the function. x^3+3x^2+x+3…

A:

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 1 using a value…

A: The two-point forward difference formula to calculate f'(x) is f'(x)=f(x+h)-f(x)h, where h is the…

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

A: Given function: y=x-12x-x2-arccosx-1

Q: If f(x)=1-x/2+x find the derivatives of f (using f'(x)=lim h-->0 f(x+h)-f(x)/h

A: The given function is fx=1-x2+x.

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: y = x*(1 – In x4)

A:

Q: Develop a general rule for the nth derivative of xf(x), where f is a differentiable function of x.

A: Given: the function xfx, where f is a differentiable function of x.

Q: a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent…

A:

Q: a, b, and I are differentiable functions of the same variable what is the derivative of H ac b +…

A: To find the derivative of acb, here a,b and c are differentiable function of same variable. Let a,b…

Q: Find the derivative of the function by the limit process. f(x) = 6/x^2

A:

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 8

A:

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: 6. Using the limit defenition of the derivative, find the equation of the line tangent to the curve…

A: We have to find the slope of the tangent line at first.Then we find its equation.

Q: 4. Find the derivative of f(x) = Vr +1 using the limit definition. (a) Find the slope of the tangent…

A: (1) The derivative from the limit definition is:…

Q: 2. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

A:

Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

A: Given: y=cosh-12x+1Here ,we havecoshy=2x+1Taking the derivatives on both…

Q: Find the equation of the line tangent to the graph of y = r-2x at the point T= 2. Use the limit…

A:

Q: Find the derivative of the function by the limit process. f(x) - f'(x) =

A: The given function is f(x)=4x2We have to find the derivative of f(x).

Q: 3) (a) Let f(x) = -x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: Given: A graph of y=fx is given.  To find:  The graph of the derivative function y=f'x over the…

Q: Find the derivative of the function.

A:

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Find the derivative of the function using chain rule. f(x) = esin?x

A:

Q: 3. Give the definition of a derivative of a function f of one variable at a point xo. /2 Find the…

A:

Q: Find the derivative of the function f(x)=1/x using limit definition derivative

A: According to the given information it is required to calculate the derivative of the function using…

Q: Find the derivative of a function at a given point F(x)= 2e^x-x at x=1 F(x)= x^3-5x at x=2

A: We have to find derivatives of the function: Fx=2ex-x at x=1 and Fx=x3-5x at x=2. We know the…

Q: Find the derivative of the function by the limit process. f(x) = 31 f'(x) =

A: The given function is fx=31.

Q: 7. Determine the derivative of the function with respect to x. ソミx

A:

Q: 13. Suppose a continuous function f and its derivative f' have values table. Given that f(1) 2, use…

A:

Q: The first derivative of a continuous function y = f(x) is y' = x(x- 21). Find y" and then use the…

A: Given: i. The first derivative of a continuous function y=fx.ii. y'=xx-212 To Find: i. y''ii. Use…

Q: If a function is increasing everywhere (and it has a derivative), then it's derivative function is…

A: explanation of above question is given below,

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

A:

Q: 1) Use the limit definition to find the derivative of the function f(x) = 6x – x². Then find all…

A: Using limits definition:f'(x) = limh→0 f(x+h) - f(x)hf(x) = 6x - x2f(x+h) = 6(x+h)- (x+h)2   = 6x +…

Q: [4] For the Basic Absolute Value function f(x) = x, (a) state its slope (derivative) function (b)…

A: The absolute value function, |x| is defined as follows. |x|=xx≥0-xx<0   The graph of |x| can be…

Q: The derivative of the function y=f(x) at the point x=c is characterized as the of the function at…

A: We have to tell what is derivative of function y=f(x) at x=c called ...  a. Slope  b. Point of…

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A: Given : what is defined as the limit of the ratio of the change in a function to the corresponding…

Q: Find all x-values where g(x) = −(x^3 )+ 3(x^2 )+ 9x − 20 has a horizontal tangent line (that is,…

A:

Q: The second derivative of an anti-derivative of a differentiable function F R-R is: O possibly…

A: The second derivative of an anti-derivative of a differentiable function f:R→R is

Q: Determine the derivative of the function with a domain {x |x # 0 and x # + nn, n E R}. sec(x) f(x)…

A:

Q: The derivative of a function intervals is decreasing ? is given by f’ (x)=e^ sin x -cos x-1 for 0 <…

A: topic - decreasing intervals of a function f is decreasing on intervals where f'(x) is negative

Q: If function f(x) is not continuous at the value x = a then the derivative of f does not exist at x =…

A:

Q: Given f(x)=x(x-1). a) Find first derivatives of function f(x) using product rule and chain rule.

A: Our objective is to find the derivative and critical points.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: