3. For f(x) = x -5x-6, make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at x = 6.

Q: 7. Find the slope of the tangent line to the graph at (1,1): x²y² – 9x² – 4y² = 0 %3D r-9r-4y = 0…

A: find the slope of the tangent line to the graph at 1,1; x2y2-9x2-4y2=0 differentiate the equation…

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: For f(x) = x3, show that the slope of the secant line over [l,x] is x 2 + x + 1, and use this to…

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

A: Solution:

Q: For the function ​f(x)=-3x^2 make a table of slopes of secant lines and make a conjecture about the…

A: It is known that the slope of a secant line between points (a, f(a)) and (b, f(b)) is given by:

Q: Find the line tangent to the graph of f(x) = x² + x +1 at xo = 2

A:

Q: 1. Determine the points where the slope of the tangent to the curve: a. f(x) = 1- 3x² is equal to 5…

A:

Q: If the slope of the tangent line to the graph of y=f(x) at x=a is m(a)=2a+1, and fl-1)=2, then what…

A:

Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

Q: Determine the slope of the tangent line to the curve (;² – 2x – 8) 2 -9 R(x) = at the point where…

A:

Q: For what value of x is the tangent line to the curve y= x2 –6x+5 horizontal?

A: We have to solve the problem

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

A: Slope of a function is the first derivative for the function f(x).So integrate the value of slope to…

Q: Given that the graph of f(x) passes through the point (7, 3) and that the slope of its tangent line…

A: Use the fact that derivative of a curve is the slope

Q: Given that the graph of f(x) passes through the point (5, 2) 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)=2x^3+9x^2+14x−12 parallel to the line…

A: Remarks; slope of two parallel line are same

Q: -2, find an If g(x) = xf(x), where f(3) = 4 and f'(3) equation of the tangent line to the graph of g…

A: Consider the given function gx=xfx

Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: 5. Find the slopes of the tangent lines to 2x? – 3xy+y³ = -1 at y = - 3.

A:

Q: Find f (3) and f' (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.

A: Tangent to a function at a point is a line which just touches the graph of the function at that…

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: Find an equation of the tangent line at x and f'(3) = 2. 3, assuming that f(3) = 5

A:

Q: 2 Find the slope of the tangent line to у 3 at X = 1 3 - х

A:

Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

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

A:

Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

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

A:

Q: What is the slope of the tangent line that touches the graph of In y + e2a-1 = 3y – 4x at the point…

A:

Q: 3. Given that the graph of f passes through the point (2,5) and that the slope of the tangent line…

A:

Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the 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: 2 For the graph of f(x) = ax + bx +4, the slope of the tangent at the point (3, 1) is 5. Determine…

A: Given that        f(x) = ax2+bx+4

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: What is the slope of the tangent line that touches the graph of In y + e2"- = 3y – 4r at the point…

A:

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: What is the slope of the tangent line that touches the graph of Iny+e2x-1 = 3y – 4x at the point A 1

A:

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

A:

Q: Given that the graph of f(x)  passes through the point (4,10) and that the slope of its tangent line…

A: Given that the graph of f(x)  passes through the point (4,10) and that the slope of its tangent line…

Q: Find the slope of the tangent to the curve x° + 4xy+ y² = 13 at (1, 2). The slope is (Enter undef if…

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 (6, 10) and that the slope of its tangent line…

A:

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

A: Solution )slop of tangent line                f'(x) = 2x + 5 Intregating both sides  ∫f'(x) =…

Q: For f (x) = x 3, show that the slope of the secant line over [ -3, x] is x 2 - 3x + 9, and use this…

A:

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

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

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

A: