Let f be the function given by f (x) = 3 sin(2x) +2 What is the approximation for f (4.5) found by using the line tangent to the graph of f at

Q: Let f(x) tangent line to the graph of f(x) at the point (0, 0) is = 6x + 15 – 15e". Then the…

A: The given curve is: f(x)=6x+15-15ex

Q: t is d

A: It is Given that function is differentiable at x=3. and f'(3)=-6 and f(3)=1

Q: The derivative of the function f is defined by f' (x) = (x² + 4) cos (x - 3). If f(6) = -1, then use…

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x +4 sin(a %3D If f(0) = 3 and f'(0)…

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Q: Does the graph of the function y = 6x + 12 sin x have any horizontal tangents in the interval…

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Q: Let f(x) = x* – 2x + 14. Then the equation of the tangent line to the graph of f(x) at the point (1,…

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Q: Find an equation of the line tangent to the graph of f at the given point.

A: Find an equation of the line tangent to the graph of f at the given point. f(x)=sin-1(x/4), (2,π/6)…

Q: Find the tangent line to f(x) given below x)f(x) = cos(X cos(x?) + 2x at x=0.

A: .

Q: Find the equation of the line tangent to the graph of f(x) = 4 sin(x) at a = T.

A: Given,          fx=4sinx at x=π.

Q: Let f(x) = V13 – x The slope of the tangent line to the graph of f(x) at the point (4, 3) is The…

A: Given ,  f(x) = √(13 - x) (A)  We have to find the slope of tangent line to the graph of f(x) at the…

Q: The derivative of the function f is defined by f'(x) = x² – x – 2 cos (x2). If f(3) = 2, then use a…

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Q: Find the equation of the tangent Iline for the function f(x) = at the point x = 1. Write in the form…

A: The objective is to find the equation of the tangent line for the function f(x)=2xx2+1 at the point…

Q: For what values of x does the graph of f(x) = x + 2 sin x have a horizontal tangent?

A: Given query is to find the values of x for which function has horizontal tangent.

Q: Determine the value(s) of x such that f(x)=e*-6x have a horizontal tangent line. Answer in exact…

A: Given that  function f(x) = e3x - 6x and we determine the value of x the function have horizontal…

Q: find the equation of the tangent line for the given f(x) at the given point f(x)=tan11(pi(x)),…

A: Given point is (1/4, 1) and given function is

Q: Let f(x) be a function that is differentiable at x = -2. Given that f'(-2) = 3 and f(-2) = 6, find…

A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

Q: Find the equation of the tangent line to the function f(x)=x2−x+2 at the point where x=−1

A: The given function is fx=x2-x+2 and the x-intercept of a point is x=-1. Evaluate the corresponding y…

Q: For what value of x does the graph of f (x) = 6sinx + sin?x have a horizontal tangent?

A: Given , fx=6sinx+sin2xWe have find the value of x for which the function have a horizontaltangent…

Q: Find the equation of the tangent line to the functions: 2. f(x)= Vx+ 2 at x= 4

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Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

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Q: V. Determine the equation of the tangent line to the graph of g at the point where r = 1 if g(x)= In…

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Q: Find the equation of the tangent line to the graph of the function f (r) = -4 z+3 at the point (0,-)…

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Q: Find an equation of the tangent line to the graph of f at the given point.            f(x) = (1 +…

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Q: Consider the function f(x) = 1/x and show it on grap. Find the equation of the tangent line at x =3.

A: Given function is fx=1x. To graph the function and the find the equation of the tangent line at x=3.…

Q: Write an equation of the tangent line to the graph of f(x) 3x at x = +1. %3D 1+2x2 For what value(s)…

A: Given that fx=3x21+2x2 Solution :fx=3x21+2x2f'x=6x1+2x2-4x3x21+2x22if…

Q: On the graph of f(x) = tanx and the interval [ − π, π ), for what value(s) of x does f(x) = 1?

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Q: The slope of the tangent line to the graph of f(x)%3D at a =-1 is: x2 - Select one: 1. a. O b. O c.0

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Q: Use the following derivative function f' to determine the local minima and maxima of the function f:…

A: Consider the provided question,

Q: Find all the values of x where the function f(x) = 5e* sin x has a horizontal tangent line.

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Q: Let f be the function with derivative given by f' (z) = sin z +I cOs z for 0 <z < 7. On which of the…

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Q: Define f = sin(px^3)+cos(qx)^2 as a function of x (with p and q constant) and differentiate with…

A: see 2nd step.

Q: 13. Determine where the graph of the function f (x) = sin(9x) is concave upward and where it is…

A: Given fx=sin9x  ,0≤x≤2π9

Q: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

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Q: 2. Consider the function f(x) = 1 – x², z ER. Draw the graph of f and calculate the equation of line…

A: solve the following

Q: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

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Q: prove that if f = sin x the derivative is df = cos x. S dx %3D

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Q: Find the relative extrema (if any) of the function f(x) = sin 2x ; over the interval (0, π).

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Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

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Q: Find the equation of the fangent line to the graph of the function f (z) sin (3,/7) at the point…

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Q: Determine the location of any horizontal tangent lines to the graph of f ( x ) = 2 sin ⁡ x − x on […

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Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 9 sin(x). If f(0) = 4 and f'(0)…

A: Given f"(x)=2x+9sinx Also f(0)=4=f'(0) We need to find f(3).

Q: For what values of x does f(x) = 3x+6 sin x have a horizontal tangent line?

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Q: Does the line tangent to the graph of f(x) = sin(2x) +5x at x = lie above or below the graph of f?…

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Q: 3) Find the slope of the curve defined by f (x) = x 3 sin x at x =r.

A: Solution -  Slope of the curve is given by df(x)dx, We have the function f(x), f(x) = x3sinx, Now…

Q: For what values of x does the graph of f(x) = 3e*cosx have a horizontal tangent line? 4.

A: Explanation of the answer is as follows

Q: Consider the following. F(x) = x In x, (-1, 0) (a) Find an equation of the tangent line to the graph…

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Q: Find the equation of the tangent line of the function at the given point. 9. f(x) = 3x+2 (0,-2) x-1…

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Q: Find the function f given that the slope of the tangent line to the graph of f at any point (x,…

A: Solution is done in step 2

Q: Find the equation of the tangent line to the function f(x) = r + 3z++4 at the point where x =-2.…

A: Given : fx = x3+3x2+x+4

Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

A: