which is the equation for a line with a rate of change of 1/3 which passes through point (-6, 3)

Q: Explain how to apply the First Derivative Test.

A: Explain how to apply the First Derivative Test.

Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

A: Given that f(x)=x2 To find two tangents that passes through (-1,-3)

Q: What are the the mean value theorem in application of derivatives?

A:

Q: What is the meaning of a derivative?

A:

Q: Describe the parallels between finding the instantaneous velocity of an object at a point in time…

A: We have to find out the parallels between finding the instantaneous velocity of an object at a point…

Q: Describe the two methods that help to differentiate the equations implicitly, and find the…

A: The two methods that help to differentiate the equation implicitly and derivative…

Q: Find the slope and equation of tangent line y=4-x^3, (-1,5)

A: Consider the given equation: y=4-x3 The point where tangent has to be calculated is (-1,5)

Q: Estimate the instantaneous rate of change of y(x) = 2x² + 2 at the point: In other words, choose…

A: To estimate the instantaneous rate of change of yx=2x2+2 at the point: x=-2.

Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

A:

Q: Explain how to apply the Second Derivative Test.

A: The second derivative test is used to find the relative maxima or relative minima. The second…

Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

Q: State the Second Derivative Test

A: Second Derivative Test:   This is used to find local extrema.

Q: What role does the derivative play in defining slopes, tangent lines, and rates of change?

A: To determine the role of derivative of a function in defining slopes, tangent lines and rate of…

Q: What function measures the rate of change of distance?

A: _____ function measures the rate of change of distance

Q: How do you find the derivative of a constant multiplied by afunction?

A: If f(x) is any function and let y=cf(x)            function f(x) multiplyed with a constant, c is…

Q: Explain why the slope of the tangent line can be interpreted as aninstantaneous rate of change

A: The average rate of change of a function fx over the interval x, x+h is the slope of the secant line…

Q: Find the derivative of: y? – 4x = 0 at point (4,4)

A:

Q: What is the equation of the normal line to the curve 2x3-2y3-9xy=2 at the point (0,1)?

A:

Q: What is curve sketching in application of derivatives?

A: We need to answer what is curve sketching.

Q: Determine an equation of the line tangent to the curve Y = 5x-4 at the point with x- coordinate 4.

A:

Q: Suppose you are climbing a hill whose shape is given by the equationz= 1000−0.01x2−0.02y2, where x,…

A:

Q: A point is moving along the circle x2 + (y − 2)2 = 26 in such a way that its x-coordinate is…

A: Given:

Q: What is the slope of the tangent line to the graph of y= x*- 3x2 + x+ 2 at x-2? What is the…

A: Given: The graph of y = x4 – 3x2 + x + 2.

Q: what is the equation of the normal line to the curve 2x3+2y3-9xy=2 at the point (0,1)?    Please…

A: Given: 2x3+2y3-9xy=2 To Determine: Equation of the normal line

Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: a point moves along the curve y=2x^2 -1. the y value decreaces at 2 units per second. what rate is x…

A: Given that a point moves along the curve

Q: value

A: We have to find the equation of lie from the given information

Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: 2. What is the slope of the line tangent to the curve 8x3 –- y² = 4 at the point (1,-2)?

A:

Q: 9. at the point (-2,1) Find the equation of the line tangent to y = 2x2 + 1

A: We will find the equation of the line tangent in the following step.

Q: derivative of

A:

Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

A:

Q: Acceleration is the first time derivative of velocity

A:

Q: Find the slope of the curve y^3+3x^2y-9y=-5 at the point (1,-1) and also find the rate of change…

A:

Q: True or False? The Linear Approximation says that the vertical change in the graph is approximately…

A:

Q: The slope of the tangent line to the curve y = 3 3 at the point (5,2) is: X -

A:

Q: Find an equation of the line tangent to the curve at the point (4, 0.4). 2Vx ソミ x+6 Equation:

A:

Q: Find the slope of the line Express the slope as a rate of change with proper unit attached

A: We know that slope is the ratio of vertical change to the horizontal change. The slope of a line…

Q: What is the slope of the tangent line passing through y = x^2 - 3x - 5 at (-1, - 1)? Kindly show…

A:

Q: y = x-12; (4,) Use the derivative feature of a graphing utility to confirm your results.

A: We will solve the following

Q: Then the derivative of

A:

Q: Find the equation of the curve for which the second derivative is 6. The curve passes through (1,…

A:

Q: What is the slope of the curve y= 2 over √x at the point (4,1)

A: To find the slope at a particular point x=a, the first derivative of the function is taken. Once the…

Q: What’s the equation of the tangent line to the curve y = 5ln(x^3 - 7) at the point (2,0)

A:

Q: The slope of the line tangent to the curve y=2x- 3 at point (1,-1) is 5

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the instantaneous rate of change cope of the tangent line to 2 (3,-2) 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Calculate the second and the third derivative of y = 5x- 9 y": y"

A: Using derivatives rule & formula.

Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.