Question
Asked Sep 2, 2019
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2n-
X
2n
3. Let f(x)- x-x
+... + xxx-ax+b. Which value for'the pair (a,b) will
X
guarantee that the x-axis will be tangent to the graph of /(x)
at x 1
A) (n,n-1)
B) (n+1,n)
C) (1,1)
D) (n-1,n)
E) (n,n+1)
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2n- X 2n 3. Let f(x)- x-x +... + xxx-ax+b. Which value for'the pair (a,b) will X guarantee that the x-axis will be tangent to the graph of /(x) at x 1 A) (n,n-1) B) (n+1,n) C) (1,1) D) (n-1,n) E) (n,n+1)

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Expert Answer

Step 1

At x=1 the graph of f(x) touches x axis. This means at x=1, f(x)=0

Or, f(1)=0

From it we get equation: a-b=1

f(x) x2n-x2n-1+...+x4-x3+x2-ax+b
Or, f(1) (1)(1)n-+...+(1)*-(1)+(1)-a(1)+b
Or, f(1) 1-a+b
Or, 0 1-a+b
Or, a-b 1
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f(x) x2n-x2n-1+...+x4-x3+x2-ax+b Or, f(1) (1)(1)n-+...+(1)*-(1)+(1)-a(1)+b Or, f(1) 1-a+b Or, 0 1-a+b Or, a-b 1

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Step 2

At x=1 tangent is x-axis, which is horizontal. So, f'(1)=0, because slop...

f (x)—х 2n-х 2n-1 +...+x*-x3+x?-ах+b
Or, f'(x)-2nx
Or, f(1)-2n(1)th-1-(2n-1)(1)-2+....+4(1)*-3(1)*+2(1)-а
2n-
1- (2n-1)x2n-2 +.+4x3-3х?+2х-а
Or, f'(1)-2n-(2n-1)+...+4-3+2-а
Or, f'(1)-[(n-1)+2-а
Or, f(1)-n+1-а
Or, 0=n+1-a
Or, a n
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f (x)—х 2n-х 2n-1 +...+x*-x3+x?-ах+b Or, f'(x)-2nx Or, f(1)-2n(1)th-1-(2n-1)(1)-2+....+4(1)*-3(1)*+2(1)-а 2n- 1- (2n-1)x2n-2 +.+4x3-3х?+2х-а Or, f'(1)-2n-(2n-1)+...+4-3+2-а Or, f'(1)-[(n-1)+2-а Or, f(1)-n+1-а Or, 0=n+1-a Or, a n

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Math

Calculus

Derivative