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Finding Derivative of a Point?
Favourite answer:g(x) = 4x² - 2x + 15 ← this is a function
g(5) = 100 - 10 + 15 = 105 → the representative curve of the function passes through (5 ; 105)
g'(x) = 8x - 2 ← this is its derivative
g'(5) = 40 - 2 = 38 ← this is in fact the slope of the tangent line to the curve at point (5 ; 105)
g(x) = 4x² - 2x + 15 ← this is the function → to calculate the derivative:
Lim [g(x₀ + h) - g(x₀)] / h
h → 0
Lim [ { 4.(x₀ + h)² - 2.(x₀ + h) + 15 } - { 4x₀² - 2x₀ + 15 } ] / h
h → 0
Lim [ { 4.(x₀² + 2x₀.h + h²) - 2x₀ - 2h + 15 } - 4x₀² + 2x₀ - 15 ] / h
h → 0
Lim [4x₀² + 8x₀.h + 4h² - 2x₀ - 2h + 15 - 4x₀² + 2x₀ - 15] / h
h → 0
Lim [8x₀.h + 4h² - 2h] / h
h → 0
Lim h.[8x₀ + 4h - 2] / h
h → 0
Lim (8x₀ + 4h - 2) = 8x₀ - 2
h → 0
g'(x₀) = 8x - 2
g'(5) = 40 - 2 = 38 ← this is the same result (above)
4 Answers1 day ago - 11Upvotes of all answers to this question
- 5Upvotes of all answers to this question
How do I solve 15^x-8+5=62 And round 3 places past the decimal?
Exponential and log equations
7 Answers2 days ago - 4Upvotes of all answers to this question
4^x-2=3 How do I solve this and round my answer 3 places past the decimal?
7 Answers2 days ago - 1Upvotes of all answers to this question
The sides of a triangle are in the ratio of 1/2:1/3:1/4. If the perimeter is 52 cm, the length or the smallest side is?
The answer is 12 cm. Could you please show me how?
6 Answers23 hours ago - 0Upvotes of all answers to this question
is x+1 a factor of the polynomial 12x^4+5x^3+3x^2-5 explain your answer?
is x+1 a factor of the polynomial 12x^4+5x^3+3x^2-5 explain your answer
6 Answers1 day ago - 5Upvotes of all answers to this question
Percentage question ?
The price of gas increases by 25%. By what percentage must a customer reduce the consumption so that the earlier bill on the gas doesn't alter?
6 Answers2 days ago - 5Upvotes of all answers to this question
If the side of a square increases by 40%, then the area of the square increases by?
The answer is 96%. Could you please explain to me how?
5 Answers1 day ago - 2Upvotes of all answers to this question
How many numbers between 100 and 300 begin or end with 2?
5 Answers1 day ago - 11Upvotes of all answers to this question
round 475,695 to the nearest thousand?
13 Answers5 days ago - 2Upvotes of all answers to this question
- 8Upvotes of all answers to this question
- 2Upvotes of all answers to this question
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Solve the equation sin(x+3)=sinx, 0=<x=<2pi to 4 decimal places. The product of the two solutions is:?
Need help with this problem pls
8 Answers1 week ago - 3Upvotes of all answers to this question
graph your equations: 2x + 3y = 7 and y=2x + 27 label them properly, including point of intersection?
Favourite answer:2x + 3y = 7 eq1 and y=2x + 27 eq2
plug in eq2 to eq1
2x + 3(2x + 27) = 7
2x + 6x + 81 = 7
8x = 7 - 81
8x = -74
x = -37/4 Answer//
solving for y at eq2
y = 2(-37/4) + 27 = 17/2 Answer//
8 Answers5 days ago - 7Upvotes of all answers to this question
how to find the area of a circle 12cm?
12 Answers6 days ago - 4Upvotes of all answers to this question
- 0Upvotes of all answers to this question
grade 12 math help?
The width of a rectangular parking lot is 61 ft less than its length. Determine the dimensions of the parking lot if it measures 240 ft diagonally.
the answers are W=sqrt111,479-61/2 ft and 61+sqrt111479/2 ft.
i got 197 for the W and 137 for the L which is wrong.
4 Answers2 days ago
