9514 1404 393
Answer:
a) 12
b) y +5 = 12(x +2)
Step-by-step explanation:
The slope of a function is its derivative.
a) The slope of y = x^3 +3 at any point is y' = 3x^2. So, at the point where x=-2, the slope of the curve is ...
m = 3(-2)^2 = 12 . . . . slope at (-2, -5)
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b) The equation of the tangent line is most easily written using the point-slope form of the equation of a line.
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y +5 = 12(x +2) . . . . line with slope 12 through point (-2, -5)
Example 1
Write y = x2 + 4x + 1 using function notation and evaluate the function at x = 3.
Solution
Given, y = x2 + 4x + 1
By applying function notation, we get
f(x) = x2 + 4x + 1
Evaluation:
Substitute x with 3
f (3) = 32 + 4 × 3 + 1 = 9 + 12 + 1 = 22
Example 2
Evaluate the function f(x) = 3(2x+1) when x = 4.
Solution
Plug x = 4 in the function f(x).
f (4) = 3[2(4) + 1]
f (4) = 3[8 + 1]
f (4) = 3 x 9
f (4) = 27
Example 3
Write the function y = 2x2 + 4x – 3 in function notation and find f (2a + 3).
Solution
y = 2x2 + 4x – 3 ⟹ f (x) = 2x2 + 4x – 3
Substitute x with (2a + 3).
f (2a + 3) = 2(2a + 3)2 + 4(2a + 3) – 3
= 2(4a2 + 12a + 9) + 8a + 12 – 3
= 8a2 + 24a + 18 + 8a + 12 – 3
= 8a2 + 32a + 27
Eight point six two is the answer
Answer:
(t•s )(x) = 4x^3 - 29x^2 + 10x - 21
Step-by-step explanation:
(t•s )(x) is the product of functions s and t:
(t•s )(x) = ( 4x^2 - x + 3)(x - 7). Applying the Distributive Property of Multiplication, we get:
(t•s )(x) = 4x^3 - 28x^2 - x^2 + 7x + 3x - 21
which needs to be simplified by combining like terms:
(t•s )(x) = 4x^3 - 29x^2 + 10x - 21
Answer:
<em>-10ab</em>
STEP BY STEP EXPLANATION
<em>2</em><em>a</em><em> </em><em>(</em><em>3</em><em>a</em><em> </em><em>+</em><em> </em><em>b)</em><em> </em><em>-3a(</em><em>2</em><em>a</em><em> </em><em>+</em><em>4</em><em>b</em><em>)</em>
<em>6</em><em>a</em><em>²</em><em> </em><em>+</em><em> </em><em>2</em><em>a</em><em>b</em><em> </em><em>-</em><em> </em><em>6</em><em>a</em><em>²</em><em>-</em><em> </em><em>1</em><em>2</em><em>a</em><em>b</em>
<em>2</em><em>a</em><em>b</em><em>-</em><em>1</em><em>2</em><em>a</em><em>b</em><em> </em><em>6</em><em>a</em><em>²</em><em>-</em><em>6</em><em>a</em><em>²</em>
<em>-10ab</em>
Hope this will help you if not then sorry :)
