A batter hits a baseball at a point 3 feet above ground at a velocity of 100 feet per second and an angle of 45°. The path of the baseball is given by the function f(x) = −0.0032x2 + x + 3where f(x) is the height of the baseball in feet and x is the horizontal distance from home plate in feet. Will the baseball clear a 10-foot fence located 300 feet from home plate?

Q: Write the equation of the tangent line to the graph of y= 8x^4-7x-1/3-x^2 at x=1 check the…

A: First we find out first derivative at x=1 which is slope of tangent line.then we use equation of the…

Q: Find the slope of the secant line to the function f(x)=x3 when x=1 and x=2.

A:

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 the tangent line to the graph of f(x) = -2(3x – 1)³ at . Show work or explain…

A:

Q: Find the points of inflection given the function: Given the function f(x) = 2x³+ 3x²-12x-9 Where…

A: For the inflection point, second derivative is equal to zero.

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 derivative of the function. y = (2x – 5)*(8x² – 5)-3

A: Derivative denotes rate of change. According to product rule, ddxf(x)g(x)=ddxf(x)g(x)+ddxg(x)f(x)

Q: Match the function from the left side to its derivative. 1. x16 -4x-5 3 a. 2. 15 b. 3. ** 15x4 с.

A:

Q: Find an equation for the line tangent to f(x)=x3 +3x2 -2x-8, at the point where x=1

A: To find the equation of the tangent line at point x = 1 for the given curve.

Q: Find the points function' that have horizontal tangents when f(x) = x°-6x 6 On the graph of the

A:

Q: Find the slope m of the tangent line to the graph of the function at the given point and determine…

A:

Q: Find the point on the curve y = sqrt x that is closest to thepoint (3,0)

A: Given curve y=x Let A(x,y)  be a point on the curve and let B(3, 0) So distance between A and B is…

Q: If f(x) = 7x2 - x³, find f'(1) and use it to find an equation of the tangent line to the curve y =…

A:

Q: For the function f (x) = 2x° – 3x2 – 12x, use the First Derivative Test to find the location of any…

A: The given function is- fx=2x3-3x2-12x To find the critical points of a function- dfdx=0…

Q: Jx + 2x f(x)=- 7х — 4х? 8.

A:

Q: Find an equation of the line that is tangent to the graph of the function f(x)= 2x and parallel to…

A:

Q: Find an equation of the line tangent to thegraph of f(x) =3/x at (2,3/2)

A: Given: y=fx=3x, 2,32 for finding of equation of tangent at given point we need slopem of tangent at…

Q: Find the derivative of the function. Provide the solution in factored form. f(x) = 2x(x³ – 2)6 %3D

A:

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: If f(x) = 2x² – 8x + 7, find the equation of the line tangent at æ = 3. Preview TIP

A:

Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: Find the equation of the line tangent to f(x)=3x2 +4x+5 at the point (0, 5)

A: Given : f(x) = 3x2 + 4x + 5 A point (0, 5)   To  find the equation of the tangent line.

Q: Find the second derivative for the function f (x) = 4e . 1 - 2x3

A: Given: fx=4ex-12x3 for finding second derivative of given, we find first derivative then find…

Q: The graph of f(x)=2x^3+6x^2−144x+6 has two horizontal tangents. what are the positive and negative…

A: See the details solution in below

Q: Find an equation of the tangent line to the graph of the function f(x) = 2x² - 4x +5 at the point…

A: Given, f(x)=2x2-4x+5

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: Determine the equation of the line tangent to the graph of f ( x ) = 3 x 2 − x + 4 at x = − 1.  Give…

A:

Q: If f(x) = 9x2 - x³, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A:

Q: Find the slope and equation of the line tangent to f (x) = x2 +9 at the point (1, 10).

A:

Q: 1 y = 8x* + 7x³ + =x² – 14x + 6 %3D -

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 equation of the secant line on the graph of the function f(x)=7x2 between the points where…

A: take x=-1 . take x=5

Q: f(x) = (x + 2)(2x² – 3) %3D

A:

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

A:

Q: What is the maximum slope of a tangent to the function f(x) = −x3 + 4x − 2?

A: Maximum slopes of tangent to function is 4.

Q: Find the derivative and simplify. f(x) = (x12 + 4x4 + 5)(2x3 - 1) f'(x) = %3D

A: Given : fx = x12 + 4x4 + 52x3 - 1

Q: Write the equation of the line tangent to the graph of f(x) = -3x² + 5x +1 at x=1 and use it to…

A:

Q: Write the equation of the line tangent to f (x): x2 – 3x + 5 at the x

A: To find an equation of the tangent line of f(x)  at the point x=0

Q: Find the slope of the line tangent to the curve f(x)=3x-2 when x-2.

A: NOTE: Refresh your page if you can't see any equations. .

Q: If f(x) = 8x2 - x3, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: The given function is f(x)=8x2-x3

Q: find the derivative of the function using only the definition.f(x)= 16x^2-3x+12

A: Initial Calculation:The variable f(x) is a function of x. The derivative of f(x) found with respect…

Q: Find the equation of the line tangent to f(x) = 4x³ + 9x – 7 when x=3. O f(x) = 135x - 288 o f(x) =…

A: Given, f(x)=4x3+9x-7 and x=3 The equation of a line in point-slope form is given by y-y1=mx-x1…

Q: If f(x) = 2x2 - 9x + 4, find the equation of the line tangent at a 2. %3D

A: Given that: f(x) = 2x2-9x+4  To find:  Equation of tangent line at x=2.

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: Find the equation of the line tangent to the graph of f(x)= x2 over (3x-4)3 at the point…

A:

Q: Find the derivative of the function. F(x) = (7x6 + 8x³)4 %3D

A:

Q: Find the higher order derivative. f"(x) = 4x2 + 9x – 16 - f(5)(x) = %3D

A: