true or false?  Continuous functions have a tangent line at all points.

Q: Use the graph to estimate the slope of the tangent line to y = x" at the given point. Verify your…

A: We have to tell the slope of the tangents through the graphs. So, for that, we will differentiate…

Q: find all relative extrema of thefunction. Use the Second Derivative Test whereapplicable. f(x)=x^{2}…

A: The given function,  f(x) =x2e-x .........................(1)  differentiate with respect to x

Q: a. Find the function f given that the slope of the tangent line to the graph of f at any point…

A:

Q: Estimate the slope of the tangent line of the function y(t) = v5t + 1 at the point t = 2. (Use…

A: Given: yt=5t+1 The slope of the tangent line at the point t=1 can be calculated as,…

Q: If a function has a finite derivative at a given point , prove that it is continuous at that point .…

A: Let any function f(x) has a finite derivative at any given point say (c) It means…

Q: Use second fundamental theorem of calculus. Find the derivative F'(x) of the function.

A:

Q: Verify the tangent line approximation of the function at the given point. Then use a graphing…

A: To Find the derivative of the function :- To find the slope of the function at (0, 2)

Q: Explain why the slope of the tangent line can be interpreted as an instantaneous rate of change. The…

A:

Q: Estimate the slope of the tangent line of the function y(t) = v4t + 1 at the point t = 1. (Use…

A:

Q: true or false?  If the second derivative is 0 at a point then the point is an inflection point.

A:

Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: Definition: "The second derivative of a function f with respect to the variable x evaluated at x = a…

A: Since the second derivative of a function f is the derivative of the derivative of function f.

Q: Does the graph of -1, х 0 have a vertical tangent line at the origin? Give reasons for your answer.

A: Answer: No. The given graph of the function cannot have a vertical tangent line.

Q: a) Prove that (arctan r 1+2 b) Using part(a), find the derivative of f (x)= arctan (208 )

A: Properties of derivative  f(g(x))=f'(g(x)) g'(x)ddxcosx=-sinxddxax=axloga

Q: Determine the point(s) at which the graph of the function has a horizontal tangent line. No chain…

A: The given function f(x) is:

Q: Find a function

A: This is very intresting question because there are so many function on an interval whose first…

Q: Estimate the slope of the tangent line of the function y(t) = V2t + 1 at the point t 1. (Use decimal…

A: We have to find the first derivative in order to find slope.

Q: Identify the equation of the tangent line of the function: f(x) = 3x at x=2

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: When we have a limit of a function f, where the variable Δx approaches zero, the expression is known…

Q: Uncover the function f shown that the slope of the tangent line to the chart of f at any point (x,…

A:

Q: Linearization based at a uses a tangent line to a curve at x=a to estimate the y-values of a…

A:

Q: Verify the tangent line approximation of the function at the given point. Then use a graphing…

A:

Q: Puestion 4. Using the definition of the derivative, show that f(x) = ifferentiable at x = -3. |2x+6|…

A: we have to show

Q: Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not…

A: The given function is fx=x.

Q: Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not…

A: We have to find  an equation of the tangent line to the graph of the function f through the point…

Q: Use the Fundamental Theorem of Calculus to find the derivative of y = cost dt %3D [NOTE: Enter a…

A: Topic = Derivative

Q: how do i estimate and list the value of x where f(x) has a horizontal tangent

A: Recall the following facts.

Q: True or False 1) The peak of a smooth curve has a vertical tangent line. 2)The tangent line…

A: Given- Consider the given statement, 1) The peak of a smooth curve has a vertical tangent line.…

Q: equation of tangent line of f(x)=5x^3+1 at x=1 is * O y=15(x-1) O y=15 x-9

A: Given: The function f(x)=5x3+1 and a point x=1

Q: 2. how does differentiability and continuity determine the derivative of functions?

A: Differentiability and Continuity

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable.

A: Given: f(x)=x+92

Q: Estimate the slope of the tangent line of the function y(t) = V5t + 1 at the point t = 1. (Use…

A:

Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)=−2sin x…

A:

Q: A point of inflection on a curve is a point where y" is positive on one side and negative on the…

A: A point of inflexion is a point at which  y'' changes its sign. It is positive on one side and…

Q: Does the graph of -1, x0 have a vertical tangent line at the origin? Give reasons for your answer.

A: Given function is fx=-1, x<0   0, x=0   1, x>0.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A:

Q: How to find the slope and equation of the tangent line to the graph of the function f at the…

A: We have to find slope and equation of tangent line to f(x) at (2,18) where f(x) is given.We have…

Q: True or false The slope of th tangent line to a dfferentiable function f at the point (2,f(x)) is

A: The slope of the tangent line to a differentiable function f at the point (2, f(x)) is

Q: true or false?  A negative derivative indicates that the curve is frowning.

A: TRUE Consider the graph for function x^3-x

Q: Find and classify the relative extrema of the function, if they exist. You MUST use the…

A: Given :fx=2xx2+1

Q: Find the general anti-derivative of f(x) = 3. + Vx on a continuous interval. Please select file(s)…

A: topic - integration

Q: Using terms like "secant line" and "tangent line", explain how evaluating f(3+ h) – f(3) lim gives…

A: This is a problem related to derivation of the general formula of differentiation.

Q: What are the intervals where the function has a positive first derivative? (d,e) (b,c) (c,d) (e,f)…

A: Recall the fact that the first derivative is positive if the function is increasing in that…

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: Use the fact that the derivative of the function f(x) = is f'(x) = - to find the equation of the…

A:

Q: Explain theorem 11—Second Derivative Test for Local Extreme Values?

A: Second Derivative Test for Local Extreme Values: Let f be a function defined on an interval I and…

Q: The straight line y=x +B is tangent to the graph of f(x) = 2^{x at the point where x = A. Find A and…

A: The staright line y=13x+B is tangent to the graph of f(x)=2x at the point where x = A, we have to…

Q: Appy the second derivative test to find the absolute maximum value on (0, 0) for f(x) = 15-4x

A: Given function is, f(x)=15-4x-250x2

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: