Please Explain Solutions Chegg! Find slope of the Secant Line for the function f
ID: 3372998 • Letter: P
Question
Please Explain Solutions Chegg!
Find slope of the Secant Line for the function f(x) = 3x 2 - 2 passing through the points (1.1) And (1.1, 1.63). (Round answer to One Decimal place.) Find Slope of secant Line for the Function : f(x) = 3.6 X 2 - 2.2 X passing through points where X = 1 & X = 1.5. (Round answer to 2 Decimal places) Approximate the Slope of the line Tangent to f(x) = 4x 2 at X = 2. (Be sure to use an increment that is small enough for the answer to be accurate to 2 Decimal places.) The Point P(1.1) Lies on Curve f(x) = X 4. Let Q(X 0,X 0 4) be an arbitory point on the Curve, & Let S be the Secant Line drawn through P & Q. Let slope of the secant line drawn through P & Q be denoted by m 5. Find m sExplanation / Answer
1)The first problem is trivial. We are given the 2 points. Thus, the slope is (y2-y1)/(x2-x1) =
(1.63-1)/(1.1 - 1) = .63/.1 = 6.3
This is already to 1 decimal place.
2)f(x) = 3.6x^2 - 2.2x
f(1) = 3.6*1^2 - 2.2*1 = 3.6 - 2.2 = 1.4
f(1.5) = 3.6*1.5^2 - 2.2 * 1.5 =
3.6 * 9/4 - 3.3 =
8.1 - 3.3 = 4.8
Then, the slope is (4.8 - 1.4)/(1.5 - 1) = 3.4/.5 = 6.8
To 2 decimal places, this is 6.80
3)f(x) = 4x^2 at 2
f(2) = 4*2^2 = 16
Then, consider, (f(2+a)-f(2))/a =
(4(2+a)^2 - 4*2^2)/a =
(16 + 16a + 4a^2 - 16)/a =
16 + 8a
To get the slope accurate to 2 decimal places rounded, then 8a < .005
Then, a < .005/8 = .000625
Let a = .0006
Then, f(2.0006) = 4*(2.0006^2) = 16.00960144
Then, the slope is (16.00960144 - 16)/(2.0006 - 2) =
.00960144/.0006 = 16.0024
This rounds to 16.00
4) Consider the slope from (1, 1) to (x0,x0^4) as x0 goes to 1
Let's write x0 as 1 + a and take the limit as a goes to 0
Then, the slope of the secant from (1, 1) to (x0,x0^4) is the slope from
(1, 1) to (1 + a,(1 + a)^4)
The slope is
((1 + a)^4 - 1)/(1+a - 1) =
(1 + 4a + 6a^2 + 4a^3 + a^4 - 1)/a =
(4a + 6a^2 + 4a^3 + a^4)/ a =
4+ 6a + 4a^2 + a^3
lim a -> 0 4+ 6a + 4a^2 + a^3 = 4