nsider the function and the value of a. f(x) = 4 – x - x2, a = 0 a) Use mtan f(a + h) – f(a) to find the slope of the tangent line man = f'(a). = lim h-0 mean b) Find the equation of the tangent line to f at x = a. (Let x be the independent variable and y be the dependent variable.)

Q: For f(x) = x3, show that the slope of the secant line over [l,x] is x 2 + x + 1, and use this to…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate Let f(x) = x. The equation of the…

A:

Q: If f(x) = 3x? - x', find f'(1) and use it to find an equa- tion of the tangent line to the curve y =…

A: f(x)= 3x2-1f'(x)=3 (2x)-0        = 6xf'(1)=6 (1 )= 6

Q: (x) = 5sinx/6sinx+4cosx The equation of the tangent line to

A:

Q: If f(x) = x° – 5x + 1, find f'(1) f'(1) = Use it to find an equation of the tangent line to the…

A: Given function, fx=x3-5x+1 Tangent is passing through (x1,y1) (1,-3).

Q: Find the equation of the tangent Iline for the function f(x) = at the point x = 1. Write in the form…

A: The objective is to find the equation of the tangent line for the function f(x)=2xx2+1 at the point…

Q: Find the equation of the tangent line to the function f(x)=2x^2−9 at the point where x=−6. Give your…

A: Calculate the derivative of the function at given point than write the equation of tangent line.

Q: Find the linear approximation of the function g(x) = 1+x at a = 0 and use it to approximate the…

A: We will find g'(x) using the power rule

Q: Let y = y(x) = x² · f(x) and suppose f(2) = 2 and f'(2) = 3, find y'(2). y'(2) The equation of the…

A:

Q: Let f(x) = 44 – x2 The slope of the tangent line to the graph of f(x) at the point (-6, 8) is - The…

A:

Q: Let f(x) = v16 – x The slope of the tangent line to the graph of f(x) at the point (7, 3) is The…

A: The slope of the tangent line to the given curve is equal to the derivative of the function at the…

Q: Q2: Find the tangent line when the function 1- y= 4+Cot x -2Sec x and point ,0)

A:

Q: Apply the product rule to find the tangent​ line, in​ slope-intercept form, of y=​f(x) at x=3.…

A:

Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: Consider the function f(x) = x² – 3x + 5. Out of all the many tangent lines of f (x), determine the…

A:

Q: Use the four-step process to find the slope of the tangent line to the graph of tl answers…

A: We can solve the question in step by step process as below

Q: Find the slope mm of the tangent line to the curve f(x)=x^3 at the point (1, 1) by using the…

A:

Q: For what values of x is the tangent line of the graph of f(x) = 6x + 18x² - 143x+ 18 rallel to the…

A: Explanation and solutions is given below....

Q: Let f=sqrt(4x+3) and find the values below  1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x)/ h)…

A: Consider the given function

Q: Given: f(x)=x2+2 find the equation of a line tangent at point P(1,3) using limits

A: To find the equation of a line tangent at point P(1,3) on below curve using limits.

Q: Show that the tangent line to the curve y = x3 at any point (a, a3) meets the curve again at a point…

A: Proof: The given curve is y=x3. Obtain the derivative of the function as follows: dydx=ddxx3…

Q: Consider the function f(x)=8x-x2 and the point P (2,12) on the graph of f. Estimate the slope of the…

A:

Q: Let f(x) = 3x^2 + x + 5. a) Find the equation of the tangent line at x = 10. b) For what value of x…

A:

Q: (2) At what point(s) will the tangent line to y = x? - 4x +3 be horizontal

A:

Q: What is the slope of the line tangent to the graph of f at (a,f(a))? Which of the following is the…

A: we have to find the slope of the tangent line to the graph of f at (a,f(a))

Q: Let f(x) = x² + 5x + 14. What is the value of x for which the tangent line to the graph of y = f(x)…

A: The slope of the tangent line to the curve is given by,…

Q: Does the graph of Sxsin(1/x), x + 0 g(x) 1o. x = 0 |have a tangent line at the origin? Give reasons…

A:

Q: Find the slopem and an equation of the tangent line to the graph of the function f at the specified…

A: Given: fx=x2x+8; 2,25 To find: Slope (m) and equation of the tangent line to the graph of the…

Q: Find all values of x for which the tangent line of f(x) = V x2 + 18x + 96 is horizontal.

A: Given that, the tangent line horizontal. That is it is parallel to x axis. The equation of the…

Q: Let f(x) = 5x + 20x². Then the equation of the tangent line to the graph of f(x) at the point (2,…

A:

Q: Find the equation of the tangent line to the function f(x)=2x2-x  at the point where x=−1. Give your…

A:

Q: The value of b makes the liney = 2x + b be tangent to the function f (x) = x² is

A:

Q: Find the equation of the tangent line to the graph of f(x) at the (x, y)-coordinate indicated below.…

A: We have to find the equation of tangent line

Q: Show that th equation of the tangent to the curve X 1승 +1-2(a 0,b + 0) at the point (a,.b) is 즈+-2 X…

A:

Q: Find the equation of the tangent line to the function f(x) = 2x? – x at the point where x form y =…

A:

Q: Q1)a) Find line that are tangent the curve x + xy - y? = 1 at the point (2,3)

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

Q: Given the function, Show that it is not continuous at (3,-1) and determine the slope of the line…

A: The function will be discontinuous at 3, -1, if  either f(3,-1) is not defined, or,…

Q: Q3 Find the equation of the tangent line to the function f(r) =x+7 at r 1. Show your work.

A: f(x) =x3 +7 Let y = f(x) = x3 +7, we have to find the tangent at x=1 , so value of y at x=1 is  f(1)…

Q: Find the slope and equation of the tangent line to f(r) = 3+3x at a 3 using the definition. %3D

A:

Q: Let f(x) = 4x + 10 – 19e". Then the equation of the tangent line to the graph of f(x) at the point…

A: Let fx=4x+10-19ex. Then the equation of the tangent line to the graph of fx at the point 0, -9 is…

Q: Find the equation of the tangent line to the function f(x)=−3x3−2x2−1 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1

Q: Find the function f given that the slope of the tangent line to the graph at any point (x, f(x)) is…

A: f'x=lnxx

Q: How do u solve for x assuming the lines which appear tangent are tangent?

A: Use angle formed by two tangents formula

Q: Compute f '(x) and find an equation of the tangent line to the graph at x = a. f (x) = x4, a = 2

A:

Q: Show, using implicit differentiation, that any tangent line at a point P to a circle with center O…

A:

Q: Use any method to find the slope of the tangent line to the graph of the function f (x) = – at the…

A: Given function is fx=1x2. To find the slope of the tangent line at x=5. Solution: The slope of the…

Q: B) Find the slope of the line tangent to the curve y = sin x at the point where x =

A:

Q: If f(x) = 2x2 - ax - a, b, c ER, then a +b – c=? 4 and the equation of the tangent line to the curve…

A:

Q: Find the equation of the tangent line to the function f(x) = r + 3z++4 at the point where x =-2.…

A: Given : fx = x3+3x2+x+4

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at =2 ? %3D B) Find the limits by…

A: