F '(x<span>) = </span>2(3x2<span> + 5) + 6x(</span>2x<span> - </span>1<span>) ... + </span>3), s(x<span>) = </span>x<span> - 4. Use the </span>product<span> rule table. below to get: r'(</span>x) = 20x + 11. s'(x<span>) = </span>1<span> ... f'(</span>x) = (x<span> - 4</span>)(20x + 11) - (5x<span> - </span>2)(2x<span> + </span>3)/(x<span> - 4)</span>2<span>.</span>First, we will distribute 2x<span> to (</span>x<span> + 5), then we will distribute </span>3<span>. ... </span>5x<span>. That is,. multiplying binomials. 6x − </span>x<span>= </span>5x<span>. Example </span>2<span>. Multiply (3x − </span>1)(x<span> + </span>2). Answer. 3x2<span> + </span>5x<span>
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See the attached picture:
Answer:
m = rate of change of the functions.
1) m = 1/2
2) m = -1
3) m = -2
4) m = 1
5) m = 2
Step-by-step explanation:
Hi there!
For the points (a, f(a)) and (b, f(b)), the rate of change between them, m, is calculated as follows:
m = f(b) - f(a) / (b - a)
Then:
1) f(x) = 1/2 x - 3
f(0) = 1/2 · 0 -3 = -3
f(6) = 1/2 · 6 - 3 = 0
m = f(6) - f(0) /( 6 - 0)
m = 0 - (-3) / 6 = 1/2
2) f(x) = -x
f(-4) = -(-4) = 4
f(2) = -2
m = f(2) - f(-4) /(2 - (-4)
m = -2 - 4 / 2 + 4
m = -6/6
m = -1
3) f(x) = x²
f(-2) = (-2)² = 4
f(0) = 0² = 0
m = f(0) - f(-2) / 0 - (-2)
m = 0 - 4/ 2 = -2
4) f(x) = x³
f(-1) = (-1)³ = -1
f(1) = 1³ = 1
m = f(1) - f(-1) / 1 - (-1)
m = 1 - (-1)/ 2
m = 2/2 = 1
5) f(x) = 2x
f(0) = 2 · 0 = 0
f(4) = 2 · 4 = 8
m = f(4) - f(0) / (4 - 0)
m = 8 - 0 / 4
m = 2
