Find the points on the graph of f(x) = 12x – x³ where the tangent line is horizontal. (Use symbolic notation and fractions where needed. Give your answer as a comma separated list or ordered pairs in the form (*, *), (*, *), (*, *)...) (x, y) = %3D

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

A:

Q: Determine the derivative of the cube root function f(x)=3√x using the limit definition.

A:

Q: use the second derivative test to find the local exterma of the function  f(x) =x3-9x2-48x+72 on R

A:

Q: Use the second order derivative test to find local exterma of the function  f(x) =x3-9x2-48x+72 on…

A:

Q: Find the slope of the tangent line to the graph of f(x) = x³ + x at x = 3 using the limits…

A: Given- fx=x3+x To find- The slope of the tangent line to the above function at x = 3 using the…

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

A:

Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R

A:

Q: Calculate the difference quotient for f(x) = 5 - x^2 at a = 4 f(x) - f(4) / x - 4 = ?   lim  f(x)…

A: Given function is f(x)=5-x2f(4)=5-42=5-16=-11 Now, difference quotient for f(x) is…

Q: Find the instantaneous rate of change of each function at the given x-value. Use the form lim…

A: a) Given that…

Q: fx て (X)

A:

Q: for f(x) = 3-x/2x+3 , find the f'(-1) using the limit definition of derivative. then use it to find…

A: f(x) = 3-x2x+3using limit defination f'(-1) = limx→-1f(x) -f(-1)x+1…

Q: Find the derivative of the function f(x)=2x2 using the limit definition.

A: Limit definition of derivative of f(x) is  f'(x)=limh->0f(x+h)-f(x)h

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: Estimate the slope of the tangent line to the graph of the following function at the point x = -6. f…

A: Given that a function f(x) and we find the slope of this graph at point x=-6. The slope of tangent…

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

A:

Q: 3. Find all -values where the graph of f(x) = x³ + 3x² + x + 3 has a horizontal tangent line.

A: Solution is given below:

Q: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: Find the equation of the tangent line to the graph of g(x) = f'(x) at x = -1 when f(x) = 5x³ + 2x² +…

A: Here, f(x)=5x3+2x2+2x

Q: Find the derivative of the function by the limit process. f(x) = x2 − 5

A: Given function is By limit definition of the derivative

Q: 3) Find the derivative of the function f(x)= x² –x+2 using the definition of the derivative (a…

A: Given:     To determine: Derivative of the function using the definition of the derivative.

Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

Q: Find the derivative y using limit  definition y=6x^2 +4x

A:

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2-5 To Find: The derivative of the given function by the limit process

Q: Find all points on the graph of F(x)=-x3+3x2-2 at which there is a horizontal tangent line.

A: Given curve is Firstly, we will find derivative of F(x) We now that slope of tangent to a curve…

Q: Determine the points at which the graph of the function has a horizontal tangent line. f(x)=…

A:

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Find the slope.

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given,          The function is fx=7x-9.

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

A:

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: f'(x) at x if f(x) = csc³(x).

A:

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

A:

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A:

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 4x − 5x2…

A:

Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

Q: The distance between the x-intercept of the tangent line to the curve y = and the x-coordinate of…

A:

Q: Find the points on the graph of f where the tangent line is horizontal.  f(x)=(x^2+8)(5-x) larger…

A:

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: The slope of the tangent to the graph 13−x2 by the limit definition.

Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

Q: Find the points on the graph of f(x)=3x-x^3 where the tangent line is horizontal.  (Use symbolic…

A:

Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

A:

Q: Use the second derivative test to locate all local extrema for the function f(x)=x3−32x2−18x. At…

A:

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

A:

Q: Use the First Derivative Test to find the x-value(s) at which the function 4 f(x) = x4 - 4x² + 1 X.…

A:

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: The slope of the tangent line m to the graph of fat the given point x0,fx0 is expressed as-…