Find a second-degree polynomial f(x) = ax² + bx + c such that its graph has a tangent line with slope 10 at the point (2,7) and an x -intercept at (1,0).

Q: at point x0=1 ,x1=1 and x2=2 f(x)=sin(x)+(x^2)+xe^2 function crossing second Write down the…

A:

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: Find the equaiton of the tangent line for the function f(x)=x+3/x-3 at the point (4,7).

A: We find f'(x) using the quotient rule.

Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: What is the maximum slope of a tangent to the function f(x) -x³ + 4x - 2? ==

A:

Q: Find the slope of the tangent line of f(x)=10x2-3 at x=-2.

A: Given f(x)=10x2-3and x=-2

Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: Write an equation of a polynomial, f, such that the second derivative test fails to determine if f…

A: Let f(x) = x3

Q: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

A:

Q: Find the equation of the tangent line to the graph of the function f (x) = /4x³ + 5 at the point…

A:

Q: Find the orthogonal trajectories for the family of curves x2 − 2y2 = C . Use a graphing utility to…

A: Concept: Trigonometry is used in finding distance and angles, there are six trigonometric ratios…

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

A: The function is given by f(x) =-2x3+6x2-3 To evaluate : The point of local maxima or local minima.

Q: Find an equation of the tangent to the curve f(x) = 2x2 - 2x + 1 that has slope 2.

A:

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: I dont know where to start this problem. It would be great to have some help

A: Given:

Q: 7. Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2x² + 3x using First…

A:

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

A:

Q: find the slope of the tangent line to the curve X2-4X3y2=-2 at the point (1,1)

A: The given curve is,

Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

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

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

A:

Q: Find an equation of the tangent line to the graph of f(x)=x^2+3x-7 at the point (1,-3)

A:

Q: slope m of the line tangent

A:

Q: Find the equation of the tangent and normal line of the function f(x)=√2x-1 at the point (5,3)

A:

Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 7x − 4x2…

A: Given, function

Q: Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line…

A:

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

A:

Q: Find an equation of the tangent line to the graph of the function f(x) = x2 + 3x +5 at point (-4,…

A:

Q: (A) Find the absolute maxima and minima for y 4x +1 over 3 - [-V5, V5]. (B) Use the second…

A:

Q: Find the equation of the tangent line to the graph of f(x) = x² – 4 at the point (3, 5). -

A: The equation of the line passing through the point (x1,y1) having slope m is given as (y-y1)…

Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A:

Q: 3. Find the slope of the line tangent to f(x) = In(4x² – 3) at (1,1).

A:

Q: Find the derivative using the long method 3-t to

A:

Q: Find the slope of the tangent line of f (x) = 2x² - 3x + 2 at x = 2 %3D

A:

Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…

A:

Q: Find the tangent and normal line to the curve at the specified condition.  3x3 - x2 - 12x + 6 at…

A: Suppose we wish to find the equation of the tangent tof(x) = 3x3 − x2 - 12x +6 the points where the…

Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Find the points on the graph of f(x) = 36x – 3x³ where the tangent line is horizontal. %3D

A:

Q: sketch the curve f(x)= ln((x^2-4)/(x^2-3x-4))

A: given curve is                                                     f(x)=lnx2-4x2-3x-4 we have to…

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

A:

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

A:

Q: Determine the area of the triangle formed by the tangent to the graph of the function y=3-x2 drawn…

A: Given,            y = 3 - x2 , and the point 1, 2

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: Find the critical points of f(x)=3x^4 -4x^3 +5 and use the first derivative test to determine local…

A: Given,          fx=3x4-4x3+5

Q: Find the equation of the line that is perpendicular to the tangent line to f(x) = x4+1 at x = 2 and…

A: Answer and explanation is given below

Q: Find the slope of the tangent line to the graph of the function at the given point. F(x) = 2x2 – 5,…

A:

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

A: