WebFind f ' (x). Solution Using the linearity rule, we see that Example 3 Let Again using linearity, f' (x) = a (x3)' + b (x2)' + c (x)' + (d)' = 3ax^2 + 2bx + c Example 3 can be generalized as … Web9. Show that if the function y = f (x) has a minimum at c, then the function y = f (x) also has a minimum at c.10. Find the point on the line y = 5 x + 4 that is closest to the origin. 11. Find the point on the parabola 2 y = x 2 that is closest to the point (− 4, 1) 12. A can is to be made to hold a litre of oil. Find the radius of the can that will minimize the cost of the …

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WebOct 18, 2015 · Solving for (f ∘ g )(x) watch fully. College Algebra getting to you? No worries I got you covered check out my other videos for help. If you don't see what ... WebFind the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.5x^4-160x^3+2; Question: Find the intervals on which f(x) is … cervisan ovuli opinioni

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WebGiven the functions f (x) = x 2 + 6 and g (x) = 2x – 1, find (f ∘ g) (x). Solution Substitute x with 2x – 1 in the function f (x) = x 2 + 6. (f ∘ g) (x) = (2x – 1) 2 + 6 = (2x – 1) (2x – 1) + 6 Apply FOIL = 4x 2 – 4x + 1 + 6 = 4x 2 – 4x + 7 Example 2 Given the functions g (x) = 2x – 1 and f (x) = x 2 + 6, find (g ∘ f) (x). Solution WebExplanation: . Using the defined function, f(a) will produce the same result when substituted for x: f(a) = a 2 – 5 Setting this equal to 4, you can solve for a:. a 2 – 5 = 4. a 2 = 9. a = –3 or 3 WebJun 8, 2024 · So, the exact equation for the first derivative is: f '(x) = 2x2 +4x + 3 We repeat the process to obtain an equation to the original function: f (x) = 2 3 x3 +2x2 + 3x +k And evaluate the function, when x = −1, knowing that the result is equal to −2: f ( −1) = 2 3 ⋅ ( −1) +2 ⋅ 1 + 3 ⋅ ( −1) +k = − 2 3 −1 +k − 5 3 + k = − 2 k = − 1 3 cervelat mit käse