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mr Goodwill [35]
2 years ago
10

Please answer i really need help

Mathematics
1 answer:
Firlakuza [10]2 years ago
7 0
X intercept is (1,0)
y intercept is (0,-4)
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6. Let f and g be differentiable functions
Julli [10]

Answer:

(b) 1

Step-by-step explanation:

To differentiate h(x)=f(x)g(x) we will need the product rule:

h'(x)=f'(x)g(x)+f(x)g'(x).

We have h'(x)=f(x)g'(x), so the following equation is true by the transitive property:

f'(x)g(x)+f(x)g'(x)=f(x)g'(x)

By subtraction property we have:

f'(x)g(x)=0

Since g(x) \neq 0, then we can divide both sides by g(x):

f'(x)=\frac{0}{g(x)}

f'(x)=0

This implies f(x) is constant.

So we have that f(x)=c where c is a real number.

Since f(0)=1 and f(0)=c, then by transitive property 1=c.

So f(x)=1.

Checking:

h(x)=1 \cdot g(x)

h'(x)=g'(x)=1 \cdot g'(x)

So the following conditions were met.

5 0
3 years ago
Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivat
patriot [66]
The given function is f(x) = x⁶(x-1)⁵

The first derivative is
f'(x) = 6x⁵(x-1)⁵ + 5x⁶(x-1)⁴
       = x⁵(x-1)⁴(6x - 6 + 5x)
       = x⁵(x-1)⁴(11x - 6)
The critical values are the zeros of f'(x). They are
x = 0, 6/11, and 1.
The critical values indicate that turning points exist for f(x) at the critical points. However, we do not know the nature of the turning points.

Write the first derivative in the form f'(x) = (x-1)⁴(11x⁶ - 6x⁵).
The second derivative is
f''(x) = 4(x-1)³(11x⁶ - 6x⁵) + (x-1)⁴(66x⁵ - 30x⁴)
        = (x-1)³(44x⁶ - 24x⁵ + 66x⁶ - 30x⁵ - 66x⁵ + 30x⁴)
        = (x-1)³(110x⁶ - 120x⁵ + 30x⁴)
        = 10x⁴(x-1)³(11x² - 12x + 3)
The sign of f''(x) at the critical values tell us the nature of the turning point.

f''(0) = 0, therefore a point of inflection exists at x = 0.
f''(6/11) > 0, therefore a local minumum exists at x = 6/11.
f''(1) = 0, therefore a point of inflection exists at x=1.

The graphs shown below confirm these results.

8 0
3 years ago
Whats the 11th term of 2,6,18,54
Natalija [7]
The 11th term would be 39,366.

The rule for this sequence is 3n (n times 3). Simplying multiplying by 3 until you get to the 11th term (54 * 3 * 3 * 3 * 3 * 3 * 3), would give you this answer.

I hope this helps!!
8 0
3 years ago
In algebraic expression<br><br> Three-fourths the square of a number.
allsm [11]

Answer:

3/4x^2

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Vitek1552 [10]

Step-by-step explanation:

cos F = HF/FG

cos 52° = x/(4.3)

0.6 = x/4.3

=> x = 4.3 × 0.6

x = 2.58

so the length of HF = 2.58 = 2.6 ft

7 0
3 years ago
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