For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find the tangent line to the graph of y=√7x+2 at x=1. Enter all values as integers, or fractions in lowest terms. y=

Q: 3. For f(x) = /2x compute the slopes of the secant lines from 16 to each of 16± 0.01, 16 +0.001, 16…

A: When x = 16, f(x) = f(16) = √(2 x 16) = 4√2 =  5.6569  hence, slope of the secant line from (16,…

Q: Find an equation of the line L tangent to the graph of f(x) = 8x +1 at x = 1/2.

A: Calculate the y-coordinate of the point where the tangent has to be drawn. Substitute 12 for x in…

Q: Find the tangent line to the function f (x) = x² – 4x + 5 at the point (3,2).

A: To find: The tangent line to function fx=x2-4x+5 at the point 3,2. Formula used: The slope of…

Q: Find the line tangent to the graph of f(x) = x² + x +1 at xo = 2

A:

Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

Q: Find the tangent line to g (x) 16 4T at z = 4.

A:

Q: Find the slope of the tangent to the curve x2 + 8xy + y = 10| at (1, 1)|

A: The equation of the given curve, x2+8xy+y2=10

Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

A:

Q: Find the point on the curve y = x-11x+5 at which the tangent has the equati on y = x - 11.

A: We will find the  point on the curve at which the equation of tangent is given as following.

Q: The tangent line to the curve il me f(a) at 2 m 1 goes through the points y=f(x) x == and Find the…

A:

Q: Find the slope of the tangent line to the curve x4+6xy+y2=17 at (1,2).

A:

Q: Find the equation of the tangent line to f-l x+4 at the point P (,0) for f(x) = 3x + 3

A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: Find an equation of the tangent line to f(x) = x° – 2x +1 at the point (0, 1).

A: The given function is: f(x)=x3-2x+1

Q: Find a > 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

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: 7) Find the tangent line to the graph of f (x) = 3 – 4e * at x =0.

A:

Q: J(x+h)-f (x) h 4x+9x+5 Problem #1: Using lim, Find the slope of the tangent line y = 3x-8 at x = -1.

A: Given: y=4x3+9x+53x−8 Let f(x) =y=4x3+9x+53x−8 We know that f'x=limh→0 f(x+h)−f(x)h Now slope of the…

Q: 3. For f(x) = x -5x-6, make a table of slopes of secant lines and make a conjecture about the slope…

A: As we know that the slope of the tangent line is given by, dydxx=a=limh→0f(a+h)-f(a)h If a = 6, then…

Q: Find the equation of the line tangent to the curve x^3 - 3xy + 4x = 2 at x = 1.

A: On solving this we will get

Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value. f(x) = (4x + 5)5…

A: Given equation of curve is as below. To find the equation of tangent line to the curve f(x) at x =…

Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

A:

Q: If y=mx+b is the equation of the tangent line to the graph of f(x)= x² - x at x= -1, then m=

A:

Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: find all points (x,y) on the graph of f(x)=3x^2-5x with tangent lines parallel to the line y=7x+1.

A:

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

A:

Q: Find the equation of the tangent line to f(x) = x^2 −3x+5 at the point x = 3.

A: Given function , fx= x2-3x+5 at the point x=3 ,at x=3 , f3= 32-3x3+5             f3=9-9+5=5Hence ,…

Q: For f(x)=3x^4, find dy/dx using the definition, dy/dx=limΔx→0 Δy/Δx= limΔx→0 f(x+Δx)−f(x)/Δx.…

A:

Q: Find the equation of the tangent line to the graph of f(x) at the given point. f(x) = /28x +21 at…

A:

Q: Find the equation of the tangent line to the function f(x)=−2x3−4x2−3x+2 at the point where x=−1.…

A:

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: दलालभ यला Find an equafion of the tangent line to the ceurve at the grven point. y=x3-3x + 1, (2,3)

A:

Q: What is the slope of the tangent line that touches the graph of Iny+e2x-1 = 3y – 4x at the point A 1

A:

Q: 5. Find the tangent line to the curve of f(x)= Vx2 +8x at x = 1.

A:

Q: Find the slope of the line tangent to the curve x^3 - 3xy + 4x = 2 at x=1.

A:

Q: Find the slope of the tangent to the curve x° + 4xy+ y² = 13 at (1, 2). The slope is (Enter undef if…

A:

Q: If y=mx+b is the equation of the tangent line to the graph of f(x) = X .2 - X at x= -1, then m= b3D

A: According to power rule of differentiation

Q: Find the equation of the tangent line to  f(x) = x2 − 2x + 2  at  x = 5.

A: The given equation is fx=x2-2x+2.

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

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

Q: For f (x) = x 3, show that the slope of the secant line over [ -3, x] is x 2 - 3x + 9, and use this…

A:

Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = (2x +…

A:

Q: Find the equation of the line tangent to the graph of f(x) = (In x)* at x=7.

A: Slope is evaluated by differentiating f(x) wrt x at x=7 . Also f(7) is evaluated. Write equation of…

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: 2. Given f (x) = x² – 2x + 5, find the tangent line at x = 7

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains…

Q: Find the equation of the tangent line to the curve f(x)=5-x² at x = 2. O x-4y-2=0 O 4x + y +7=0 O 4x…

A: Find the equation of the tangent line to the curve f(x) =5-x^2 at x=2.