For which value(s) of x does f(x)=8x3/3 +5x2 −10x+15 have a tangent line of slope −7? If there is more than one answer, give all of the x-values separated by commas, e.g. if f(x) has a tangent line of slope −7 at x=3 and x=5 enter 3,5.

Q: 3. For f(x) = /2x compute the slopes of the secant lines from 16 to each of 16± 0.01, 16 +0.001, 16…

A: When x = 16, f(x) = f(16) = √(2 x 16) = 4√2 =  5.6569  hence, slope of the secant line from (16,…

Q: Given that the graph of f(x) passes through the point (4, 5) and that the slope of its tangent line…

A:

Q: 3. Determine the value of b if the slope of the tangent to f(x) = (3x² + 1)(2x² + b) at x =– 1 is –…

A: given,       fx=y=3x2+12x2+b    slope of the tangent, at x=-1      dydx=-16

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

A:

Q: Given that the graph of f(x) passes through the point (2, 2) and that the slope of its tangent line…

A: Solution:

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

A:

Q: Find h'(-2) if h = f • g, f(x) = -6x2 – 4 and the equation of the tangent line of g at -2 is y = -9x…

A: Slope of y=-9x+6 is = -9 This line is tangent to g at x=-2  So we get: g'(-2)= -9   The tangent line…

Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

A:

Q: The product of all the values of x for which the tangent lines to the graph of y= are parallel to…

A:

Q: The equation of the tangent line to f(x) = 5x2 + 7 at x = 0 is a y = 5x + 7 b y = 7 y = 2x + 14 O d…

A:

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: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

A:

Q: Find the slope of the line tangent to the curve x - 3xy + 4x = 2 at x = 1. -5/3 O 2/3 O 1/3 O 4/3

A: The given curve is: x3-3xy+4x=2 We need to find the slope of the line tangent to the given curve.…

Q: Find all values of x for which the tangent line of f(x) x2 + 18x + 96 is horizontal.

A: fx=x2+18x+96 Differentiating with respect to x, we get f'x=ddxx2+18x+96=12x2+18x+96·dx2+18x+96dx…

Q: For what values of x is the tangent line of the graph of f(x) = 2x – 6x² – 48x + 18 %3D parallel to…

A:

Q: The equation of tangent line to the graph of 8x²+16y²=48 at (2,1) is A x- y - 3=0 x- y+3=0 c none of…

A: Slope of tangent line is y'

Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

Q: For what values of x is the tangent line of the graph of f(x)=2x^3+9x^2+14x−12 parallel to the line…

A: Remarks; slope of two parallel line are same

Q: Find the points on the graph of x^2+2x+4y^2=4+y where the tangent line is horizontal

A:

Q: 5. Find the equation of the line tangent to the graph of f(x)= 2x' +4x² – 5x– 3 at | x = -1.

A: f(x)=2x3+4x2-5x-3diff w.r.t xf'(x) =6x2+8x-5now substitue x=-1f'(-1)=6(-1)2+8(-1)-5f'(-1)=-7slope of…

Q: For which value(s) of x does f(x)=4x2+5x+17 have a tangent line of slope 4?If there is more than one…

A: f(x)=4x2+5x+17 Slope of the tangent is given by dy / dx = f'(x)So, we will have to differentiate the…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

A:

Q: For what values of x is the tangent line of the graph of f(x) = 6x + 18x² - 143x+ 18 rallel to the…

A: Explanation and solutions is given below....

Q: 1. Find the slope of the line tangent to the graph of f (x) = x³ In (x² – 5x + 7) at x = 2. - Do NOT…

A: We have to find slope to given equation by derivative.

Q: What is the slope of the tangent line to the graph of any quadratic function of the form y=ax²+bx+c…

A: First find the vertex of the parabola, y=ax2+bx+c . Then, compute the expression for dydx .…

Q: Given that the graph of f(x) passes through the point (7, 6) and that the slope of its tangent line…

A:

Q: The slope of the tangent line to the graph of the function y = 8Vx – 3 at (9, 21) is %3D 1.33 -2.33…

A:

Q: Given that the graph of f(x) passes through the point (5, 2) and that the slope of its tangent line…

A:

Q: Given that the graph of f(x) passes through the point (4, 9) and that the slope of its tangent line…

A:

Q: Given that the graph of f(x) passes through the point (8,10) and that the slope of its tangent line…

A:

Q: Find all values of x for which the tangent line of f(x) = / x² + 18x+96 is horizontal.

A:

Q: Given that the graph of f(x) passes through the point (5,10)( and that the slope of its tangent line…

A: Given , The graph of f(x) passes through the point (5,10) and that the slope of its tangent line at…

Q: Given that the graph of f(x) passes through the point (4, 2) and that the slope of its tangent line…

A: Recall: The slope of the tangent line to the curve f(x) is f'(x).

Q: Given that the graph of f(x) passes through the point (8,9) and that the slope of its tangent line…

A: Given the slope of the tangent line of graph of y=f(x) at (x,f(x)) is 6x + 2, so dydx=6x+2 Now solve…

Q: The slope of the tangent line to f(x) = 3x² – 1 at x = 2 is 12. true false

A: The solution of the problem is given in the next step.

Q: Find X values of all points on the graph of g=x²³ + 3x² -11x +5 where the slope of tangent line is 3…

A:

Q: Find the slope of the line tangent to the curve x^3 - 3xy + 4x = 2 at x=1.

A:

Q: For what values of x is the tangent line of the graph of f(x) = 6x^3 + 9x^2 −218x   parallel to the…

A:

Q: If the curve is defined by y= x⁴ - 8x³ + 22x²-24x+9, then what are the value/s of x for which the…

A:

Q: Given that the graph of f(x) passes through the point (5,6) and that the slope of its tangent line…

A:

Q: For what values of x is the tangent line of the graph of f(x)= 2x3-12x2+2x+18 parallel to the line…

A: The tangent line of the graph of f(x)= 2x3-12x2+2x+18 is parallel to the line y=2x+.4 So, slope of…

Q: Given that the graph of f(x) passes through the point (2, 4) and that the slope of its tangent line…

A: Explanation of the answer is as follows

Q: 3. Determine the value of b if the slope of the tangent to f (x) = (3x² + 1)(2x² + b) at x = – 1 is…

A: The formula to find the slope of the tangent to the function f(x) is f'(x).

Q: 1. Find the equation of the tangent line to f(x)= 4x2 - 5x+2 at (-1,11).

A: We can find the equation of tangent to the curve as below.

Q: Given that the graph of f(x) passes through the point (8, 2) and that the slope of its tangent line…

A:

Q: 2. Given f (x) = x² – 2x + 5, find the tangent line at x = 7

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains…

Q: 3. Find the equation of the tangent line to the graph of x²y + 9xy= 162 at the point (-3, 6).

A:

Q: Given that the graph of f(x) passes through the point (7, 6) and that the slope of its tangent line…

A: Let y=f(x) is the curve. The curve passes through (7, 6) and slope of tangent at (x, y) is 4x+5.…

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: