Linear Approximations
It's the linear approximation for
f(x)=x^3-x^2+3 \text{ at } a=-2
f(x) \approx 16x+23
It's the increasing and decreasing intervals of f(x) where
f'(x)=(x-1)(x-2)^2(x-3)
f increasing on
(-∞, 1) ∪ (3, ∞)
f decreasing on
(1,3)
Find the relative extrema of
f'(x)=(x-1)(x-2)^2(x-3)
local min at x = 3
local max at x = 1
It's the intervals where the function is concave up and concave down for
f(x)=x(x+5)^2
concave down on
(-∞, -\frac{10}{3})
concave up on
(-\frac{10}{3}, ∞)
Find the inflection point (x-value) for
f(x)=x(x+5)^2
inflection point at
-\frac{10}{3}
I have a face but no eyes, hands, but no arms. What am I?
It's the linear approximation for
f(x)=x^{1/3} \text{ at } a=8
f(x) \approx \frac{x}{12}+\frac{4}{3}
It's the increasing and decreasing intervals of f(x) where
f(x)=x^4-6x^2+5
f increasing on
(-sqrt(3), 0) ∪ (sqrt(3), ∞)
f decreasing on
(-∞, -sqrt(3)) ∪ (0, sqrt(3))
Find the relative extrema of
f(x)=x^4-6x^2+5
local min at
x=+-sqrt(3)
local max at
x=0
It's the intervals where the function is concave up and concave down for
f(x)=x^4-6x^2+5
concave up on
(-∞, -1)∪(1, ∞)
concave down on
(-1, 1)
Find the inflection point (x-value) for
f(x)=x^4-12x^2
inflection points at
x=-sqrt(2),sqrt(2)
I am a seed with three letters in my name. Take away the last two and I still sound the same. What am I?
Pea
It's the linear approximation for
f(x)=(1+x)^r \text{ at } x=0
1+rx
It's the increasing and decreasing intervals of f(x) where
f(x) = ln(x^2+4)
f increasing on
(0, ∞)
f decreasing on
(-∞, 0)
Find the relative extrema of
f(x) = ln(x^2+4)
local min at x = 0
no local max
It's the intervals where the function is concave up and concave down for
f(x) = ln(x^2+4)
concave down on
(-∞, -2)∪(2, ∞)
concave up on
(-2, 2)
Find the inflection point (x-value) for
f(x) = ln(x^2+4)
inflection point at x=-2, 2
I am a mother from a family of eight. Spins around all day despite my weight. Had a 9th sibling before finding out it's fake. What am I?
Earth
It's the linear approximation for
f(x)=1+e^{3x} \text{ at } a=0
f(x) \approx 2 + 3x
It's the increasing and decreasing intervals of f(x) where
f(x) = \frac{3x}{ln(x)}
f increasing on
(e, ∞)
f decreasing on
(-∞, 1) ∪ (1, e)
Find the relative extrema (coordinates) of
f(x) = \frac{3x}{ln(x)}
no local max
local max at (e, 3e)
It's the intervals where the function is concave up and concave down for
f(x) = (5x+30)^(\frac{2}{3})
No concave up intervals
concave down on
(-∞, -6)∪(-6, ∞)
Find the inflection point (x-value) for
f(x) = (5x+30)^(\frac{2}{3})
no inflection points
I can be never stolen from you. I am owned by everyone. Some have more, some have less. What am I?
Knowledge
It's the linear approximation for
f(x)=\arctan x \text{ at } a=0
x
It's the increasing and decreasing intervals of f(x) where
f(x) = \frac{1}{x^2+1}
f increasing on
(-∞, -2) ∪ (-2, 0)
f decreasing on
(0, 2) ∪ (2, ∞)
Find the relative extrema (coordinates) of
f(x) = \frac{1}{x^2-1}
no local min
local max at (0, -1)
It's the intervals where the function is concave up and concave down for
f(x) = \frac{1}{x^2+1}
concave up on
(-∞, -2)∪(2, ∞)
concave down on
(-2, 2)
Find the inflection point (x-value) for
f(x) = \frac{1}{x^2+1}
no inflection points
I am the only thing that places today before yesterday. What am I?
Dictionary