Find the interval where the graph of y = x3 + 2x2 − 4 is decreasing and concave up.

Q: The local linear approximation for f (x) = Vx2 + 16 near x = -3 is

A:

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: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

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

A:

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

A:

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 4 – 3 x, and the line…

A: Given: f(x)=4-13x If the given line is y=mx+c with slope m then the slope of a line perpendicular to…

Q: Find the equation of the line tangent to the graph of f(x) = 6x° + 5x² – 4x – 7 at x = -3

A:

Q: Find the length y=(x+2)^3/2 for x in the range 0≤x≤2.

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: Find the slope of the secant line connecting the points on the graph f(x)=2h+4x-12, with the given…

A:

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 point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: Find a formula for the linear function f(x) with slope 2 and vertical intercept 1. f(x) =

A:

Q: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

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

A:

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 point on the curve y = /2x + 3 which is closest to the point (5, 0).

A:

Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: In this question given that two line which are intersect each other and and a line is perpendicular…

Q: Find the equation of the family of curves whose slope at any point (x,y) is 3x2+4

A: To find: the equation of the family of curves whose slope at any point (x,y) is 3x2+4  We know that…

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: Find the point at which the line f(x) = - x – 2 intersects the line g(x) 3x + 6 %3D

A: f(x) = g(x) Thus, -x-2 = 3x + 6   Separate variables to LHS and constants to RHS -x-3x = 6 + 2 -4x =…

Q: Find the slope of the curve y=x4 at x=3.

A: Find the slope of the curve y=x4  at    x=3.

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 point on the graph of the function that is closest to the given point. f(x) = Vx - 4, (15,…

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 point of inflection of the curve x^3 – 3x^2 –x + 7.

A: For inflection point, second derivative is zero

Q: Find the area of a triangle bounded by the y axis, the line f(x)=8−13x, and the line perpendicular…

A: Recall : Area of the triangle with three points x1,y1,x2,y2 and x3,y3 :            A=…

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

Q: Find the slope of the curve y = 2x2-3x at point (1,3) O 2 O 3 O -2 0 1

A: We   have to find slope

Q: The region in the first quadrant bounded by the x-axis and f (x) = 3x – x² is

A: The graph of region bounded by curves y=3x-x^2 and x-axis is

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: Find the point on the graph of the line f(x)=3x+4 that is closest to the point (6,3) x= y=

A:

Q: Graph the function ƒ(x) = 8 + 2x - x2 anddetermine the values of a and b that maximize the value of…

A: Consider the function  ƒx=8+2x−x2

Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: 2) Sketch the graph of the floor function f(x) = x+31 over the interval [-4,2].

A:

Q: The line y=3x+6 is tangent to the graph of y = (-48)/(x-6) at the point ?

A: The given equation of tangent is y=3x+6 and its tangent to graph of y=-48x-6. To find the points at…

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

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: Find the equation of the line tangent to f(x) = 4x³ – 5x +4 at (–2, –18). -

A:

Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: find the length of the curve y = 2x6+1/8x2 from x is greater than or equal to 1 and less than or…

A:

Q: Find the point on the graph of f(x) = Vx that is closest to the point (5, 0). (x, y) =

A: Use distance between point concept and then differentiate

Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

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

A:

Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

A:

Q: 4) Where is the function g(x) = 3x2 -x+ 5 differentiable?

A:

Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

A:

Q: Find the y-intercept of the line tangent to y=(x' – 4x² + 8)en * at x = 2. а. -21.032 b. -2.081 с. 0…

A: Topic:- Application of Derivative  Correct option = d