3. Let Ax) = - 2 (x + 2)² (x – 1)'. Do not use your calculator until part e. a. List the x-intercepts of f(x) and describe the graph at each (touch or pa. b. Find the y-intercept of f(x).

Q: Find all points of the graph of f(x) = 3x2 + 9x whose tangent lines are parallel to the line y - 57x…

A: Solution: Two lines are parallel if they have same slope.

Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

A:

Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: Find an eqaution of the line tangent to the graph f(x) = 3x2 - 5x at the point (1,-2).

A: fx=3x2-5x Slope of the tangent line is the derivative of the given function at the given point. So…

Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

A:

Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

A:

Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

A:

Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

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 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 all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

A:

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: Find the equation of the tan gent line to the graph of the equation f(x) = 5x - 8x +12, at the point…

A: Here we are going to solve only one question and for the remaining question post the question again.…

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: Find the point on the graph of y = 3x2 − 2x + 5 where the tangent line is perpendicular to the line…

A:

Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: 3. Find the slope of the graph tangent to the curve y =x* - 2x3 +x that passes through the point (2,…

A:

Q: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

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

A: The function is given by fx = 4x3+6x2-6x-5 To evaluate: The equation of the tangent line to the…

Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: Use the derivative to find the vertex of each parabola y = ax2 + bx + c

A: Given the function y = ax2 + bx + c We need  to use the derivative to find the vertex of  parabola.

Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

A: The points where the tangents are horizontal are the points at which slope is zero.That means,…

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: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: 4. Find the slope of the line tangent to the graph of 1 f (x) = 2x4 – 32x3 + 17x2 – 9x + 4 at x 2 -…

A:

Q: Find the equation of the line tangent to the graph of f(x) = −2x² + x + 3 at x = 1. Provide your…

A:

Q: Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions…

A: Given that, z=3x2+y2+3xy-7x-8y+10 Subject to  x-y≤200 2x+y-150≤250

Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

A:

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

A:

Q: B. Find the length of the curve y = x² from x 0 tox = 4.

A:

Q: End the Vellue of g) if the slope of the Curve y= x-2x is (2)?

A:

Q: 1) Find the slope of the linels) tongent to the graph of (y+x)²-y =x² at X=0.

A:

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

A: The solution are next step

Q: Graph the Ine whose x-tercept is -I and whose y-intercnpt is 1.

A: Given,           The line whose x-intercept is -1 and y-intercept is 1.We know that,           The…

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A:

Q: Suppose that the graph of x = f(y) lies to the left of the y-axis. Is f(y) dy positive or negative?

A:

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: 4. Jacobi is seated on the line tangent to the graph of  y =2x3 -3x2 -12x +21 at x =2.

A:

Q: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

A:

Q: What is the slope of the tangent line that touches the graph of In(y) + eA-=3y-4x at the point 3. 5

A:

Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

A:

Q: Find the point where the tangent to the graph of f(x)= -x^2-6 is parallel to the line y=4x-1

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Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: At what point does the graph of the function f(x) = x³ – 3x has horizontal tangent ? Find equations…

A: a) Points are (1,-2) and (-1,2) b) Lines are y=-x-1, and y=-x+3

Q: 2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

A: