4. Suppose f(x) = 4x3-x* a) Find all intercepts. b) Find the intervals where f(x) is increasing and where it is decreasing. 10 c) Find the intervals where f(x) is concave upward and where it is concave downward.

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

A: Let S be an open set containing , and let f be a function of two variables defined on S, except…

Q: What is the equation of the curve that passes through the point (1, 3) and has a slope of 2 x+3 O 9…

A: Here we have to write the equation of the curve that passes through the point (1,3) and has a slope…

Q: What is the equation of the line tangent to * f(x) = 4x2 + 2x – 1 at x = 0

A:

Q: Find the equation of the line tangent to the graph of y = 2x - 8x2 + 2x -6 at x = 2. | %3D

A:

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

A:

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=9−27xf(x)=9-27x, and the line…

A:

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 the curve y=ax3-bx2-cx-3 at x=2 is 5. If the point of inflection of the curve is at…

A: The slope of the curve y=ax3-bx2-cx-3 at x=2 is 5. If the point of inflection of the curve is at…

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: Arc length is defined as the distance between two points on the curve. It is done in such as way…

Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: Find the points on the graph of f (x) = x3 − 3x2 + x + 4 where the tangent line has slope 10.

A:

Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

A:

Q: The slope of the tangent line to the graph of the function y = 9Va -2 at (4, 16) is -5.00 O -4.00 O…

A: Simply calculate the derivative of function at given point.

Q: The line y = -4x + 16 is tangent to the graph of 100 y : x + 6 at the point help (points)

A: Given the equation of a tangent line:

Q: Find the equations of the line that is tangent to f(x) = x3 - x2 +3x - 4 at x = 2

A:

Q: What points is the function y=|5x-1|+7sin(7x) continuous?

A: we have given function y=5x-1+7sin(7x) we know that  sin(ax) is continuous everywhere hence sin(7x)…

Q: Suppose that f(x, y) = 3xª + 3yª – 2xy Then the minimum is

A:

Q: What is the length of the curve y = sqrt(4-x2) from x = -2 to x = 1?

A: y=4-x2 Differentiating with respect to x, we get dydx=124-x2·d4-x2dx   ∵dxdx=12x=124-x2·0-2x=-x4-x2

Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

A:

Q: 4)Solve for the family of curves of straight lines with y-intercepts thrice as their corresponding…

A:

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

A:

Q: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

A:

Q: Find the equations of the line that is tangent to f(x) = x4 - 3x² + 2 %3D at x 2

A: To find: The equation of the line that is tangent to f(x)=x4-3x2+2 at x=2. Calculation: The first…

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: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

A:

Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

A:

Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: Find the equation of the line tangent to the graph of f(x) = 7x³ + 8x² – 2x – 6 at x

A: We need to find the equation of the tangent to the function f(x) = 7x3+8x2-2x-6 at x=—2 We know that…

Q: (1, if x 2

A: Using the given piece wise function, we can plot it in given intervals.

Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

Q: Find the slope of the curve at the point (2,3) * x³ 2x + 1 3/2 1 O 1/2 O 1/4

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: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

A:

Q: 4. Find the equation for the line tangent to (persamaan garis şinggung) a. y= x2- 3 x + 5 at the…

A: The objective of the question is determine the equation of the tangent line.

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

A:

Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

A:

Q: Suppose that / (3r-x²) dr=Ax³+ Bx+C, for constants A, B, C. What is the value of C if the curve…

A: The given integral ∫3x4-x2dx=Ax5+Bx3+C

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: What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=O?

A:

Q: 2 5. Write the equation of the line tangent to y=4-x when x=-1.

A:

Q: What is the slope of the line tangent to the curve y = x4 – 8x3 + 22x2 – 24x + 9 at x = 1?

A:

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

A:

Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

A:

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

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

A:

Q: 4. At what points on the curve y = 2x³ – 3x2 – 2x + 4 are tangents of slope 10?

A:

Q: 2. Estimate the slope of ffx) at the point: a) where x = 3 b) where x = 2 f(x) 4 2 1 2 3 4 5 6 3. 1.

A:

Q: write the equation of the tangent and normal line line of the curve. huow somtion your 1 . f(x) = -…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.